Earlier, Pakistan's final wicket fell when Mohammad Asif (29) skied a catch to mid-on off Nathan Hauritz in the fourth over after tea. Pakistan added only four runs after the break as Asif and Umar Gul (38 not out) compiled a 53-run tenth-wicket stand.
Hauritz finished with 3 for 96 and Katich grabbed 3 for 34.
Hauritz picked up his 50th Test wicket when Asif skied a slog to Mike Hussey at mid-on to end a 53-run last-wicket stand.
Simon Katich picked up three wickets with his left-arm wrist spin after being introduced when the Pakistanis were cruising at 4-213.
Opener Salman Butt top-scored with 102, while Shoaib Malik made 58 and Umar Gul 38 not out.
The unlikely spin of Katich provided the breakthrough for Australia after lunch. It took the left hander just two overs to get his man, removing yesterday's run-out villain Salman Butt (102) with an edge to first slip, just six balls after the Pakistani notched his century.
Katich struck again in his next over, dismissing Sarfraz Ahmed caught at slip for one run to swing the game firmly in Australia's favour.
Butt's morning partner Shoaib Malik, staunch in his intent to bat for time and frustrate the Australians, finally played a loose shot off Nathan Hauritz in the next over, miscuing while trying to heave across the line and spooning the ball to Doug Bollinger at mid-on.
Katich's hot streak continued three overs later as Mohammed Aamer threw his wicket away with a wild swing that handed an easy catch to Shane Watson.
Earlier, Butt resiliently held out the Australian bowling on the third morning at Bellerive Oval.
He led the way as Pakistan went wicketless through the opening session to be 158 for 4 at lunch on day three of the third Test.
The left-handed opener (74 not out) and former skipper Shoaib Malik (28 not out) fought hard to combine for 64 more after resuming at 94 for 4 in reply to Australia's mammoth 519 for 8 declared.
It was the fourth wicketless session out of seven in the Test after Ricky Ponting and Michael Clarke amassed a 352-run stand on the opening two days on the benign Hobart wicket.
Branded a lazy and selfish runner by captain Mohammad Yousuf on Friday night after he contributed to the run outs of Yousuf and Umar Akmal, Butt did his best to atone for his sins.
The 25-year-old played the ball late and gained most of his runs from cuts off the back foot against Australia's tight bowling.
The only half-chance he gave the Australians was an edge off allrounder Shane Watson which flew low to the right of Marcus North at first slip.
North was unable to clutch the nick before it hit the ground but the edge was in striking distance of wicketkeeper Brad Haddin who didn't make a play at the ball.
Butt brought up his half-century with a clip to the square-leg boundary off Peter Siddle.