Katich stole the show with a scintillating 126 off 159 balls as NSW reached 396 and Victoria were three without loss at stumps on the third day, chasing an unlikely 455 runs for victory on Monday's final day.
Former Test skipper Steve Waugh was involved up in another mid-pitch bungle with Dominic Thornely.
Waugh set off for a quick single which Thornely showed no interest in. Waugh turned on his heels and bolted back to the bowlers' end but a direct hit from David Hussey caught him short of the crease.
Waugh disagreed with the umpire's decision, hesitating before returning to the pavilion for 31, shaking his head as boos rung around the ground.
Katich has 772 runs from five Shield games at an average of 111.28. He has 405 runs from five Tests at 67.5 highlighted by last week's maiden ton against India.
Thornely safely reached his maiden first-class century: a composed innings of 143 in more than three hours.
In Adelaide, young South Australian fast bowler Mark Cleary took four quick wickets in skittling Tasmania for 207 on the opening day of their match at Adelaide Oval.
At stumps, SA were 25 for one in reply, with opener David Fitzgerald (11) dismissed by left-arm spinner Xavier Doherty on the last ball of the day, and Shane Deitz not out on 12.
Wicketkeeper Sean Clingeleffer, Tasmania's top scorer with 42, and tailender Andrew Downton (19) produced the best partnership of the Tasmanian innings, a 60-run eighth-wicket stand to prevent a complete disaster.
Cleary finished with 4-41, sharing the spoils with Shaun Tait, who took 3-61 and all-rounder Mick Miller, who claimed 2-25.
MacGill's spell keeps NSW's hopes alive