Alexander made it 71 converted penalties from his last 76 attempts
Burnley bucked a dismal run of 10 away games without a win to overturn League One MK Dons in the FA Cup third round.
Mathias Doumbe's trip on Steven Fletcher gave the reliable Graham Alexander the chance to stroke the Clarets ahead from the penalty spot.
Fletcher found the net himself soon after as he raced on to Chris Eagles' well-weighted pass.
Wade Elliott and Fletcher both hit the woodwork before MK Dons substitute Dean Morgan pulled one back near the end.
With two points separating the Clarets from the Premier League relegation zone and manager Owen Coyle linked with the vacant manager's job at Bolton, the visitors began the match looking refreshed by the challenge of the Cup.
After Alexander had beaten Willy Gueret via the inside of the post to put the visitors ahead, it took a despairing challenge from a home defender to block Robbie Blake's goal-bound effort.
Fletcher's well-struck low shot gave Burnley breathing space going into the second half and both Elliott's long-range effort and Fletcher's header had Gueret beaten before coming off the frame of the goal.
Paul Ince's side only sparked into life in the closing stages.
Peter Leven and substitute Luke Chadwick both stretched goalkeeper Brian Jensen, before Morgan rifled in from Jude Stirling's cross.
MK Dons manager Paul Ince told BBC Three Counties Radio:
"I said to them after the game that it was a pleasure to watch. It is a pleasure for me to be the manager of that team, the way they played.
"Disappointing when you analyse, and note that the two goals came from our mistakes. We went two down but had been the better team.
"I can go back tonight and think the future is bright for Milton Keynes."
90:00+4:51 The game is over, as the referee blows his whistle.
90:00+1:35 Peter Leven concedes a free kick for a foul on Chris Eagles. Free kick taken by Michael Duff.
88:53 Jude Stirling provided the assist for the goal.
88:53 GOAL - Dean Morgan:MK Dons 1 - 2 Burnley Dean Morgan grabs a goal from close in high into the middle of the goal. Milton Keynes Dons 1-2 Burnley.
87:12 Substitution (Burnley) makes a substitution, with Steven Thompson coming on for Steven Fletcher.
86:01 Aaron Wilbraham fouled by Michael Duff, the ref awards a free kick. The free kick is delivered left-footed by Peter Leven
from left channel, save by Brian Jensen.
85:11 Unfair challenge on Wade Elliott by Luke Chadwick results in a free kick. Brian Jensen takes the free kick. The assistant
referee flags for offside against Chris Eagles. Free kick taken by Willy Gueret.
84:08 Shot by Jason Puncheon from outside the box goes high over the crossbar.
80:37 Peter Leven takes a shot. Save by Brian Jensen.
79:19 Substitution Jude Stirling on for Luke Howell.
79:19 Substitution Jermaine Easter goes off and Dean Morgan comes on.
76:16 Outswinging corner taken left-footed by Jason Puncheon from the left by-line, clearance made by Wade Elliott.
76:02 Jason Puncheon takes a shot. Blocked by Graham Alexander.
74:38 Corner taken by Jason Puncheon, Wade Elliott manages to make a clearance.
74:00 Steven Fletcher is ruled offside. Mathias Doumbe restarts play with the free kick.
73:35 Luke Chadwick has an effort at goal from 12 yards. Save by Brian Jensen.
71:34 The assistant referee signals for offside against Chris Eagles. Direct free kick taken by Willy Gueret.
71:08 Peter Leven takes a shot. Save by Brian Jensen.
70:15 Substitution Joey Gudjonsson is brought on as a substitute for Kevin McDonald.
69:02 Corner taken right-footed by Robbie Blake from the left by-line, save made by Willy Gueret.
64:14 Robbie Blake produces a shot on goal direct from the free kick, save by Willy Gueret.
64:14 Booking Booking for Jermaine Easter for unsporting behaviour.
63:43 Unfair challenge on Graham Alexander by Jermaine Easter results in a free kick.
63:15 Corner taken by Robbie Blake played to the near post, clearance by Dan Woodards.
63:01 Robbie Blake decides to take the corner short.
62:51 Christian Kalvenes delivers the ball, Luke Howell gets a block in.
61:51 Unfair challenge on Andre Bikey by Aaron Wilbraham results in a free kick. Brian Jensen restarts play with the free kick.
61:30 Luke Chadwick fouled by Richard Eckersley, the ref awards a free kick. Direct free kick taken by Dean Lewington.
59:28 The ball is sent over by Chris Eagles, Header from inside the area by Steven Fletcher bounces off the post.
55:43 Mathias Doumbe gives away a free kick for an unfair challenge on Steven Fletcher. The ball is crossed by Robbie Blake, Steven
Fletcher produces a header from inside the area that goes over the crossbar.
55:18 Foul by Aaron Wilbraham on Andre Bikey, free kick awarded. Graham Alexander takes the free kick.
54:38 Substitution Luke Chadwick is brought on as a substitute for Sam Baldock.
51:05 Effort from inside the area by Jason Puncheon misses to the left of the target.
49:32 Dan Woodards gives away a free kick for an unfair challenge on Steven Fletcher. Robbie Blake fires a strike on goal direct
from the free kick.
48:27 Robbie Blake restarts play with the free kick.
48:27 Booking Mathias Doumbe booked.
48:13 Free kick awarded for a foul by Mathias Doumbe on Christian Kalvenes.
47:36 Free kick awarded for an unfair challenge on Chris Eagles by Peter Leven. Wade Elliott takes the direct free kick.
45:42 Foul by Aaron Wilbraham on Michael Duff, free kick awarded. Brian Jensen takes the direct free kick.
45:01 The second half has started.
45:00+1:26 The half-time whistle blows.
45:00+0:34 Corner taken by Jason Puncheon.
42:36 Free kick awarded for a foul by Luke Howell on Robbie Blake. The free kick is delivered right-footed by Robbie Blake from
39:06 Effort on goal by Jason Puncheon from long range goes over the bar.
37:26 Inswinging corner taken left-footed by Jason Puncheon, Brian Jensen makes a save.
37:10 Shot by Dan Woodards. Brian Jensen makes a save.
35:18 Foul by Andre Bikey on Aaron Wilbraham, free kick awarded. Shot on goal comes in from Jason Puncheon from the free kick, save
made by Brian Jensen.
34:14 The assist for the goal came from Chris Eagles.
34:14 GOAL - Steven Fletcher:MK Dons 0 - 2 Burnley A goal is scored by Steven Fletcher from the edge of the penalty box to the bottom left corner of the goal. Milton Keynes
Dons 0-2 Burnley.
33:13 Robbie Blake has a drilled shot. Blocked by Luke Howell.
29:31 Chris Eagles delivers the ball, save by Willy Gueret.
24:24 Unfair challenge on Chris Eagles by Luke Howell results in a free kick. Robbie Blake crosses the ball from the free kick right-footed
from left wing, clearance by Luke Howell.
22:32 Steven Fletcher provided the assist for the goal.
22:31 GOAL - Graham Alexander:MK Dons 0 - 1 Burnley Placed penalty scored by Graham Alexander. Milton Keynes Dons 0-1 Burnley.
21:31 Steven Fletcher fouled by Mathias Doumbe, the ref awards a Penalty.
20:10 Inswinging corner taken left-footed by Jason Puncheon from the right by-line, clearance by Steven Fletcher.
19:38 Corner taken by Jason Puncheon from the left by-line, clearance made by Steven Fletcher.
18:38 The offside flag is raised against Steven Fletcher. Indirect free kick taken by Willy Gueret.
17:11 Shot from just outside the penalty area by Luke Howell misses to the left of the target.
16:54 The ball is delivered by Chris Eagles, clearance made by Luke Howell.
15:43 The ball is swung over by Robbie Blake, Willy Gueret makes a save.
14:42 Robbie Blake produces a right-footed shot from just outside the box that misses to the right of the net.
13:37 The offside flag is raised against Steven Fletcher. Willy Gueret takes the indirect free kick.
13:07 Unfair challenge on Graham Alexander by Peter Leven results in a free kick. Direct free kick taken by Andre Bikey.
11:02 Free kick awarded for a foul by Kevin McDonald on Jason Puncheon. Jason Puncheon restarts play with the free kick.
10:42 Aaron Wilbraham is penalised for handball and concedes a free kick. Brian Jensen takes the free kick.
9:25 Effort on goal by Aaron Wilbraham from 20 yards. Brian Jensen makes a save.
8:11 Graham Alexander challenges Sam Baldock unfairly and gives away a free kick. Free kick crossed by Peter Leven. Aaron Wilbraham
is flagged offside by the assistant referee. Brian Jensen restarts play with the free kick.
5:20 Stephen Gleeson has an effort at goal from outside the penalty box missing to the wide right of the target.
4:40 Free kick awarded for a foul by Andre Bikey on Aaron Wilbraham. Free kick taken by Jason Puncheon.
3:52 Jermaine Easter gives away a free kick for an unfair challenge on Andre Bikey. Free kick taken by Brian Jensen.
3:12 Christian Kalvenes challenges Jermaine Easter unfairly and gives away a free kick. Jason Puncheon restarts play with the free
2:40 Foul by Chris Eagles on Luke Howell, free kick awarded. Jason Puncheon restarts play with the free kick.
1:15 Centre by Wade Elliott, clearance by Mathias Doumbe.
0:00 The match has kicked off.
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