Australia need another 40 runs to get past the follow-on figure of 352 at 312 for five in reply to England's imposing first innings of 551 for six declared.
At the close on Sunday, Michael Clarke was on 30 and Adam Gilchrist on 13.
England has dominated the Test since winning the toss on Friday, but still have to close the deal on a docile pitch that has offered nothing to the bowlers.
Eleven wickets have fallen in three days with a total of 863 runs scored.
"I think Michael Clarke looked terrific and Gilly's (Gilchrist) started off really well so the first hour tomorrow is going to be crucial for us," Ponting said.
"If they can get a good partnership then we're going to be right back in the game.
"We just have to keep batting and get a little way in front and try and bowl them out as the best way (to win) at the moment.
"If we can get somewhere near their total or maybe a little bit in front that would be great."
Ponting said he may declare behind the first innings in a bid to gamble on winning on Tuesday's fifth and final day.
"We might do that if we lose early wickets in the morning," he said.
"We've still got Brett Lee and Warney (Shane Warne) to come. They're more than capable on that sort of wicket because as we've seen there's not much happening at all for the seamers and there's certainly not much for the spinners either.
"If there's something there that we can think we can chase we'll have a go at it for sure, but it all just depends on that first hour tomorrow," he said.
Ponting became Australia's pinnacle Test centurion with his 33rd hundred in his knock of 142.
It was 31-year-old Ponting's 10th century in his last 13 Tests -- he has played in 107 in all -- and took him past previous captain Steve Waugh's 32 centuries off 168 Tests.
Ponting now ranks outright all-time fourth behind Sachin Tendulkar (35), Brian Lara and Sunil Gavaskar (both 34) as the scorer of most hundreds in Tests.
But he does not reflect on his personal cricket milestones.
"I don't think about that at all, I've never been one for stats. I just don't pay attention to that at all," he said.
"I know a lot of other players carry stats around in their bags and check out how they're going and compare themselves to other players, but that's something that's just never concerned me.
"I think all players when they finish playing look back and measure themselves against other players but hopefully I've still got a few more years in me yet."