When Stokes finally hit the winning runs, the ground erupted as a famous Test match heist was achieved. My thoughts immediately turned to Edgbaston 2005, when England won another close Ashes Test, but that time it was the ball eventually conquering the bat.
At Edgbaston in 2005 England won by two runs; at Headingley in 2019 they scraped home by one wicket. In 2005 it was England's strong-man allrounder Andrew Flintoff who claimed the Player-of-th- Match award with seven wickets and 141 runs in a dazzling performance.
In 2019 the award went indisputably to the highly competitive, never-say-die England allrounder Stokes, who claimed four wickets and scored 143 in the match.
Flintoff's influence was spread throughout the match; 68 and 73 with the bat and three and four wickets with the ball. Stokes, on the other hand, saved his supreme effort until the last, plundering 135 not out, including the bulk of the 76 needed for victory when the ninth wicket fell.
After three Tests in 2005, the situation was one Test win each and a draw - exactly the same as today.
However, in 2005, it took a monumental innings at Old Trafford by Ricky Ponting - the best I've seen to save a match - to maintain the equilibrium after three Tests. And therein lies the major difference between these two enthralling series - the quality of the batting.
To be fair, the batsmen in the 2019 series have faced challenging pitches, especially when you consider the quality of the bowling.
In 2005, England passed 400 three times, and on two other occasions they cleared 300 comfortably. It's hard to imagine the current flawed line-up attaining such heights.
For their part, Australia didn't reach 400 in the series but they came close four times. That's surprising when the batting line-up included such high-class performers as Ponting, Matthew Hayden, Damien Martyn, Michael Clarke, Justin Langer and Adam Gilchrist.
There was also class in an England line-up that featured Andrew Strauss, Michael Vaughan, Kevin Pietersen, Ian Bell and Flintoff. It says something about the quality of both bowling attacks that those high-class line-ups were contained to such an extent.
Another difference in the two absorbing series is the availability of the Decision Review System in 2019. This is not necessarily progress. The flaws in the DRS have been amply displayed in this Ashes series, the most controversial being Australia's senseless waste of a review, meaning they had no comeback when Stokes was adjudged not out to Nathan Lyon with only two runs required for an England victory.
This highlights the fact that reaching the right decision - something the ICC declared was its intention when the system was introduced - is not guaranteed when you have a finite number of reviews.
Even worse was the dismissal of Marnus Labuschagne at Lord's when he was caught close to the ground by Joe Root. This was referred to the third umpire and, as is usually the case, certain angles appeared to show the ball may have touched the ground before reaching Root. This is flawed evidence because of the foreshortening effect of television and should never be utilised to decide catches.
As a result of this flaw, crowds tend to boo the fielder, visualising him as a cheat and the batsman is then likely to distrust the fielder. Both those unwarranted eventualities could be avoided if slow-motion replays weren't used to decide catches.
Controversy aside, if the 2019 series continues to provide a similar level of drama and tension to the magnificent 2005 Ashes contest, then we'll all be well and truly entertained. The 2005 Ashes - along with the 1960-61 tied Test series between Australia and West Indies - is the best I've witnessed for both quality and excitement.