Ponting went into this match needing just 25 runs to surpass former captain Border's mark of 11,174 runs and move up into third place in the all-time list of Test run-scorers behind Sachin Tendulkar (12,773) and Brian Lara (11,953).
The Tasmanian, resuming on 17 not out in Birmingham at Edgbaston, required just eight more runs Friday and an uncertain clip off his legs for three off Andrew Flintoff saw him to the record in 22 fewer matches than the 156 it had taken Border to compile his career total.
However, on 38, Ponting became Graham Onions's third wicket when he mishooked a bouncer from the Durham quick through to wicket-keeper Matt Prior.
Australia were subsequently bowled out for a modest 263, Onions taking four wickets and fellow swing bowler James Anderson five.
At stumps England, 1-0 ahead in series, were 116 for two, 147 runs behind.
And that meant for Ponting breaking Border's mark was a "bitter-sweet " experience. "It's obviously something I'm proud of," Ponting told reporters.
"I've been around a long time and been fortunate enough to break a few milestone along way. But there's a bitter-sweet taste after getting past the record but not getting a big score."
He added: "We've all dreamt of doing something like this, I'm proud of my longevity, records like this are going to come your way if you play this many games and play reasonably well.
"But never did I think I would be breaking Allan Border's record because so many things have to fall into place."
Ponting, now aged 34, was a schoolboy fan when Border was rebuilding the shattered Australia team of the mid-1980s and turning them into the all-conquering side they would become in the 1990s.
Ponting said Border's gritty example was one he'd tried to follow throughout his career.
"He was a really tough competitor, the one always playing the captain's innings when required," Ponting explained.
"He typfied an Australia player. He was hard-nosed and when things were at their toughest he stood up to be counted.
"For all of us who grew up watching cricket in that era, we've known only one way to play the game. Tough and uncompromising, that's the way I've always tried to play and I hope all the guys I've played with would say the same."
Border, also a former Test selector, paid tribute to Ponting in a statement issued by Cricket Australia.
"Clearly, I am a great admirer, having been involved in Ricky's selection in many great Australian sides, and having enjoyed watching him closely on more occasions than I can remember as a cricket media commentator as well.
"It is not just the number of runs he has made, it is how he has made them as a dominant force, leading from the front and scoring at a rate previous champions would have regarded as unthinkable".
The fact Ponting has played in the same era as India's Tendulkar and now retired West Indies star Lara, allied to Australia's general dominance of Test cricket in that period, has tended to obscure his greatness as a batsman.
Yet Ponting's average is higher than both that of Tendulkar and Lara while, when it comes to Test centuries, he is only four behind Tendulkar's world record of 42.
Leading Test match run-scorers (player, country, career dates, matches, innings, not outs, runs, highest score, average, 100s, 50s):
Sachin Tendulkar (IND) 1989- 159 261 27 12,773 248no 54.58 42 53
Brian Lara (WIS) 1990-2006 131 232 6 11,953 400no 52.88 34 48
Ricky Ponting (AUS) 1995- 134 225 26 11,188 257 56.22 38 46
Allan Border (AUS) 1978-1994 156 265 44 11,174 205 50.56 27 63
Steve Waugh (AUS) 1985-2004 168 260 46 10,927 200 51.06 32 50
Note: Ponting still has second innings of 134th Test to come.