The left-handed opener made 100 and shared a stand of 191 with skipper Ricky Ponting (89) before the hosts declared their second innings on 219-5.
It left Pakistan to chase a victory target of 438 but they lost both openers with only 29 on the board.
Shane Watson then took two wickets to reduce them to 103-4 at the close.
The hosts began the day on 59-1 knowing that three solid sessions would bring them tantalisingly close to a record-equalling 12th successive Test victories over their opponents.
Ponting and Katich enthusiastically set about building their lead on a batting track that remained benign for much of the day.
But the captain had his scares and survived when a caught-behind decision off Mohammad Aamer was referred to the video umpire on 62.
Katich was finally removed as he reached triple figures and Ponting followed before he could become only the seventh Test player to post a century and double century in the same match.
