The Hoops were knocked out of the Scottish Communities League Cup semi-final by St Mirren at Hampden last Sunday but there was little chance of another shock this week, although the breakthrough did not come until the 56th minute when Commons scored from the spot after he was fouled by Raith defender Simon Mensing.
Irn-Bru First Division side Rovers ran out of steam and in the 82nd minute Forrest, on for Tony Watt, grabbed the second goal, with Mulgrew's fine strike four minutes later completing a solid afternoon's work by the visitors.
There was a shout for a penalty in the sixth minute when Mulgrew's cross was blocked by Raith defender Eddie Malone, using his arm according to the visitors, but referee Steven McLean was not convinced.
On the half-hour mark Raith, in a rare attack, had a penalty claim of their own turned down when back-tracking midfielder Joe Ledley nudged Jason Thomson in the box to end a surging run by the Kirkcaldy defender. Again referee McLean was unimpressed.
Early in the second half, Adam Matthews' right-footed drive from outside the box cleared the Raith bar only by inches, and when the right-back turned provider with a cross on to Watt's head, the Celtic striker's effort went just wide of the far post.
In the 53rd minute, after Beram Kayal had tripped Malone 25 yards from goal, Celtic goalkeeper Lukasz Zaluska saved Brian Graham's curling free-kick down at his left-hand post with defender Kelvin Wilson completing the clearance.
Two minutes later Celtic made the breakthrough when Mensing clumsily tripped Commons inside the box and the Scotland midfielder slammed the spot-kick low into the net.
The game stretched further in the final stages and when Celtic broke with pace Forrest's first touch from Gary Hooper's pass took him into the Raith box and he confidently knocked the ball past David McGurn.
Mulgrew, who had missed a penalty in the defeat by St Mirren, curled in a third with four minutes remaining to ease the Parkhead side into the quarter-finals.