Trailing 3-0 in the four-test series, Dravid's unbeaten 146 helped India put on 197 for its final five wickets in a respectable first-innings 300. But after 379 minutes at the crease, Dravid had to walk straight back out to open the second innings and fell in the 13th over for just 13.
Sachin Tendulkar, who is still chasing his 100th international century, was unbeaten on 35 at the close as India finished on 129-3 in reply to England's 591-6 declared.
England should take the remaining seven wickets on Monday's final day but will have to work hard on a good batting pitch after India scored 326 runs for the loss of eight wickets on Sunday.
"Some of us have had a tough series but hopefully tomorrow it is Sachin's day," Dravid said. "If the other guys can rally around him maybe we can save this test."
The tourists' miserable performance on the rain-affected third day hinted at an early capitulation on Sunday, but the Indian fans in the south London crowd finally had something to cheer as Dravid picked his strokes with composure to become just the third Indian opener to finish a completed innings unbeaten.
"Obviously, from a team perspective, the series has been unsatisfactory for us," Dravid said. "It's not a nice feeling."
The 38-year-old Dravid resumed the day on 57 and survived a run out on 61 before hitting three contrasting boundaries - slog-sweeping, cutting and clipping Graeme Swann off his pads - and a single in one over to move to 99.
He made it to his century next over with a late cut for 2, raising his arms in celebration during each run.
The first player to face 30,000 deliveries in test cricket, Dravid moved above Sunil Gavaskar and Brian Lara in the all-time list of century makers and means he has 461 runs for the series, more than twice as many as the next best Indian batsman.
England's Kevin Pietersen alone has 533 for the series - 58 more than Mahendra Singh Dhoni, Tendulkar and Virender Sehwag combined.
But Pietersen, who scored 175 for his 19th century in this match, is some way behind Dravid in terms of hundreds. Only Tendulkar, Jacques Kallis and Ricky Ponting have scored more test tons than Dravid.
Without Dravid, who now averages 110.75 at The Oval, India's series would have been even more comprehensively poor.
He hit 103 in a 196-run defeat at Lord's and 117 in a 319-run defeat at Trent Bridge. When Dravid made a total 40 in two knocks at Edgbaston, India lost the only match in which he failed to make three figures by the enormous margin of an innings and 242 runs.
Only Gavaskar and Sehwag have previously carried their bat for India.
But Dravid's vigil was finally ended by Swann shortly after tea. The makeshift opener had already survived one shout for a close catch off Swann - replays confirming a not-out decision by showing the ball had hit pad instead of bat - when he fell in a similar incident.
Swann's delivery took an inside edge, hit Dravid's pad and flew toward Alastair Cook, who swatted the ball out of the air and took the catch at the second attempt. Swann then ended a typically carefree knock by Sehwag for 33, taking out his middle stump with a ball that had pitched well outside offstump.
Anderson completely beat VVS Laxman to take out his offstump for 24, leaving him with just 182 runs from eight series innings. Tendulkar then should have been out stumped by Matthew Prior for 34 when the Little Master's foot was in the air as the bails came off, but no-one - including the wicketkeeper - appealed for a review.
"I'm at the bowlers end, so I can't see that far," Swann said. "The six men around the bat are supposed to be aware of that.
"It was a tough day slogging away in the sun. It was a long, tough day. But we didn't have any designs on winning the game today."
Amit Mishra, whose first-innings 43 at least reduced the prospect of another embarrassing innings defeat, was the other unbeaten batsman at the close with 8.
India had resumed its first innings on 103-5 after a rain-interrupted third day but, after 10 overs without a breakthrough, England captain Andrew Strauss turned to paceman James Anderson.
With his 10th delivery of the day, Anderson followed an inswinger with an outswinger that caught the outside of Dhoni's bat and carried comfortably into the waiting gloves of Prior, dismissing the India captain for a 50-ball 17.
"The bowling attack has been very good," Dravid said. "They have swung it at pace and the wickets have been challenging as well.
"They have been pretty spicy wickets."
Tim Bresnan finally got a wicket for his persistence with the dramatic intervention of Ian Bell - who had already put his stamp on the match with his 235 in England's total.
Mishra mistimed a pull shot and Bell took a spectacular one-handed catch high to his right at short leg to end Mishra's sixth-wicket stand with Dravid at 87.
Opener Gautam Gambhir made a hesitant 10 runs at No 9 after sitting out Saturday with a mild concussion sustained the previous day while dropping Pietersen, who went on to make 175. Stuart Broad caught the bat with a rising short ball and Gambhir's attempted fend dropped kindly to Pietersen, who stepped forward from the slips to take the catch.
RP Singh swung the bat around, mixing in the occasional clean shot with his full-blooded swipes to score 25 from 23 balls with five boundaries.
But Bresnan had Mishra caught by Anderson in the slips above his head and then lured last man Sreesanth into a drive to Eoin Morgan at short cover to finish with 3-54.
