The 24-year-old quick was named man-of-the-match for his three for 41 in Australia's seven-wicket Super Eights victory against England here at the Sir Vivian Richards Stadium as his table-topping team moved a step closer towards the semi-finals.
Tait beat England captain Michael Vaughan (five) and the recalled Andrew Strauss (seven) for pace, the experienced duo both playing on.
He then returned in the middle of the innings to maintain the pressure by having Paul Collinwgood, a thorn in Australia's side during England's 2-0 CB series finals win in February, caught behind for two.
Often criticised for his waywardness, Tait was noticeably more accurate than in previous games and Ponting said his strike bowler was following a similar path to Lee, who didn't make it to the Caribbean because of an ankle injury.
"The pleasing thing in Shaun being man-of-the-match is that he took a look at his bowling in the first few games and found an area or two where he could change things around a little bit.
"It's great to see the younger guys working on their games and getting some results out of it," said Ponting who backed up Tait's efforts with an 86 that helped see Australia, chasing 248, win with 16 balls to spare.
Tait, who has now taken 11 wickets at under 23 apiece this tournament, added: "I've been a bit disappointed throughout the tournament with my first few overs of every game.
"I haven't been hitting my straps quite like I should be. I've been disappointed with the wides I've been bowling with the new ball, but I controlled it a lot better today."
Ponting said there was no reason why, with veteran seamer Glenn McGrath due to retire after the World Cup, Tait and Lee couldn't play in the same one-day side.
"I'd love to have both guys in my team if they are going as well as they can. Glenn's obviously finishing up so a bowling spot's open.
"Brett's got away from the out-and-out strike bowler he's always been labelled as. Tait is that for us at the moment. But the more he plays the more he'll understand the ways to go about bowling in different conditions.
"Brett's a bit more advanced, he understands his game very well. He's taking wickets but doesn't go for runs. That always plagued him early in his career, when he was going around six an over but he's got that down a lot in the last few years.
"He's been the best bowler in the world in one-day international cricket for some time."
Ponting said that while England had provided Australia with their "biggest test" at the tournament they should have provided an even sterner challenge.
"They should have made 270-280, no question.
"I'm not sure what it is about us. Brad Hogg (Australia's lone specialist spinner) got us a crucial breakthrough (having Andrew Flintoff stumped for four), as did Shane early on and McGrath through the middle."
Australia next play surprise package Ireland in Barbados on Friday and Ponting insisted: "There's still some improvement to come, we haven't played our best cricket yet."