The 37-year-old, who has repeatedly faced down calls to quit, overtook Rahul Dravid's 13,288 by the narrowest of margins -- a single run -- when he was out for 23 on day one at Windsor Park, Roseau.
The former Australian captain, who compiled his 13,289 in 165 matches, now trails only India's Sachin Tendulkar in the all-time list. The "Little Master" is on 15,470.
"My love for the game and passion and desire to play and be successful hasn't changed," said Ponting on Sunday, the eve of the final Test, when asked if he was considering quitting. "Even when things were really tough a few months ago, all I wanted to do was try to give myself the best chance to be able to play well again.
"I felt I got there through the summer and I feel like I'm batting really well at the moment. I've still got a few things I want to achieve and a few games of cricket I want to be a part of and win for Australia. "As long as I feel I can play a role winning games of cricket for Australia I'll continue to do it. I'm enjoying it as much as ever and probably working harder than ever on my game."
Ponting had previously scored four, 14, seven and 41 in the three-Test series, renewing questions about his future.
The World Cup-winner was axed from Australia's one-day set-up in February, despite roaring back from a lean spell by averaging 108.80 in the 4-0 Test sweep of India. But he received backing from captain Michael Clarke, who said runs had been hard to come by on the Test tour which Australia lead 1-0.
"He's hitting the ball well, probably hasn't got that big score that he'd like but none of us have. Conditions haven't been great for making big hundreds," Clarke told www.cricinfo.com. "If you wanted to make runs here you had to bat for a hell of a long time, and need a bit of luck as well along the way.
"Ricky's one of the guys that has put the team above himself and sacrificed his wicket or tried to take the game forward because we've needed to, to try and help us win the game."
