Jim McIntyre headed home United's first goal
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Grant Brebner scored his first Dundee United goal as Clyde were swept aside in the CIS Insurance Cup.
Striker Jim McIntyre headed in an Andy McLaren cross after 34 minutes to settle the home side.
Barry Robson added a fine strike from 18 yards right on the half-time whistle and the same player crossed for Brebner to head home after 54 minutes.
Mark Wilson fired in a 61st minute penalty after Stuart Balmer was judged to have handled the ball.
United gave Canadian international Lars Hirschfeld his first start, in place of regular goalkeeper Tony Bullock, who broke his collarbone at the weekend.
He was called into action as early as the ninth minute and had to be grateful to David McCracken for clearing off the line after Ian Harty skipped around him inside the box before firing a shot on target.
Clyde created the better early opportunities and had another great chance to open the scoring on 20 minutes when McCracken sliced Gary Arbuckle's dangerous low cross wide.
McIntyre headed a good chance over from six yards and soon after found the mark, when a wicked McLaren cross from the right eliminated the Clyde rearguard.
Visiting goalkeeper Bryn Halliwell then expertly tipped Robson's powerful shot over the bar and had to look smart to deny McIntyre.
Clyde's early spirit appeared to have been sapped and they made their task doubly difficult by conceding an 18-yard Robson drive just as referee Dougie McDonald was about to blow for the interval.
The men from Lanarkshire found themselves three down 10 minutes after the break.
Robson whipped in a delightful right-foot cross for Brebner and the former Hibs man
dived in ahead of everyone to open his Tannadice account.
Halliwell kept his side within a respectable distance of their hosts by saving Wilson's powerful free-kick but was picking the ball out of the net again seconds later after a penalty awarded for Balmer's handball.
The Scotland Under-21 man stepped up to take the kick and, as he did against Aberdeen a fortnight ago, blasted it beyond the goalkeeper's left hand into the far corner.
Dundee Utd: Hirschfeld, Wilson (Dodds 69), McCracken, Innes, Archibald, Duff, McInnes, Brebner, Robson, McLaren (Scotland 64), McIntyre (Samuel 73). Subs Not Used: Jarvie, Kerr. Booked: McCracken.
Goals: McIntyre 35, Robson 45, Brebner 55, Wilson 64 pen.
Clyde: Halliwell, Mensing, Balmer, Potter, Walker, Arbuckle, Sheridan, Gibson (Bryson 57), Marsiglia (McKeever 64), Wilford, Harty. Subs Not Used: Morrison, Gilhaney, McCracken.
Attendance: 2,336
Referee: D McDonald