Celtic swept to victory at St Mirren Park, despite resting three of their midweek Champions League heroes.
Brown, Vennegoor of Hesselink and McDonald all scored
Scott Brown fired the opener from close range after 22 minutes and Scott McDonald poked the second over the head of St Mirren goalkeeper Chris Smith.
Jan Vennegoor of Hesselink headed the third after the break, then Derek Riordan's attempt at a low cross deflected in off Marco Miranda.
Stephen McManus stabbed in the fifth before Miranda replied from 20 yards.
The result appeared to justify Celtic manager Gordon Strachan's decision to freshen up his midfield following the emotional Champions League qualifying victory over Spartak Moscow.
Shunsuke Nakamura was a surprise omission along with Aiden McGeady and Massimo Donati, with their places being taken by Evander Sno, Paul Hartley and Derek Riordan.
St Mirren boss Gus MacPherson also made three changes following the shock home defeat by Third Division East Fife in the CIS Insurance Cup.
Out went Billy Mehmet, Richard Brittain and Alex Burke and in came Alan Reid, Garry Brady and Stewart Kean.
A dull start to the match was given some light relief by a comically petty incident after 12 minutes.
Strachan ran on to the pitch to recover objects that appeared to fall from the Celtic physio's bag as he ran on to treat Lee Naylor.
But, after fourth official Dougie McDonald spoke to Strachan for encroaching, the Celtic boss ran back on the pitch and dumped them back on the grass.
Marco Miranda (left) scored St Mirren's consolation goal
McDonald was then forced to remove the articles during the next break in play.
The match itself was ended as a contest with two goals within four minutes.
McDonald was tackled on the edge of the box, the ball deflected into the path of Brown and the midfielder toe-poked the ball under Smith from 10 yards.
The Australian striker then pounced on some indecision in the St Mirren defence following a long ball out of defence from Mark Wilson.
Defender John Potter looked slow to react and, as Smith raced off his line into no-man's land, McDonald flicked the ball over the goalkeeper's head and into the unguarded net.
St Mirren squandered a great chance when Miranda's superb curling cross found Mark Corcoran unmarked 12 yards out.
But the striker strangely chose to chest the ball towards goal and the effort failed to trouble goalkeeper Artur Boruc.
The ineffectual Sno was replaced with Donati at half-time and another two quickfire goals ensured Celtic's victory.
Vennegoor of Hesselink rose at the front post to head home a Riordan corner after 53 minutes.
Recent Buddies signing Miranda, whose performance was the one bright spot on a black day for the home side, was unlucky to deflect Riordan cross past Smith.
And, when Riordan failed with two attempts to beat Smith, McManus swept home the fifth from close range.
Miranda showed his quality by stepping inside a challenge and driving the ball superbly past Boruc, whose legs prevented Corcoran from further reducing the arrears from close range.
St Mirren: Smith, van Zanten, Reid, Haining, Potter, Mason (Birchall 61), Murray (Brittain 80), Miranda, Brady, Kean (Mehmet 54), Corcoran.
Subs Not Used: Howard, McCay, Barron, McGinn.
Goals: Miranda 75.
Celtic: Boruc, Wilson, Naylor, McManus, Caldwell, Sno (Donati 46), Hartley, Riordan, Scott Brown, McDonald (Zurawski 70), Vennegoor of Hesselink (Killen 64).
Subs Not Used: Mark Brown, Nakamura, McGeady, O'Dea.
Goals: Scott Brown 22, McDonald 25, Vennegoor of Hesselink 53, Miranda 56 og, McManus 74.
Ref: K Clark