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Gambhir, 27, who top-scored with 179 in the first innings, fell for 97 before India declared their second innings on 251 for seven after lunch.
England were 64 for one when play was called off as a draw after tea, after the visitors were set an improbable victory target of 403 in 43 overs.
Gambhir was dismissed by a brilliant diving catch at point by Ian Bell, who also ran out Yuvraj Singh for 86 with a direct hit to dash his century hopes.
India skipper Mahendra Singh Dhoni delayed the declaration to help both batsmen reach hundreds until they succumbed to Bell, who also ran out opener Virender Sehwag (17) on day four.
The match was badly curtailed by poor visibility due to fog.
"We lost around 80-90 overs, it gets really tough (to win) because the wicket was good," Dhoni said. "If you see the first two days there was a bit of moisture in the wicket.
"I think England bowled really well," he added. "After that, the wicket saw sun on the day and it got better to bat on."
Gambhir hit his ninth Test fifty to sign off a brilliant year and Yuvraj his fourth. The pair shared a 153-run fifth wicket partnership to revive the innings from 80 for four.
The Delhi batsman hit six fours in his five-and-half hour innings, facing 229 balls while Yuvraj scored his runs off just 93 deliveries, hitting six fours and four sixes.
Fog forced a two-and-a-half hour delay to the start of play, leaving a victory for the hosts unlikely in the game hit by poor visibility on each of the five days.
Yuvraj hit off spinner Graeme Swann for seven runs in an over to reach his fifty, studded with four sixes, before lunch.
He hit three sixes in the morning, lashing James Anderson over midwicket and then two in succession against paceman Stuart Broad, including a stunning shot over cover.
However, Bell beat him with a direct hit attempting to regain his crease after he blindly took off for a single after pushing left-arm spinner Monty Panesar to backward shortleg.
Gambhir's 276 runs in the match is the highest aggregate by an Indian batsman in a Test against England, surpassing the 257 by Vinoo Mankad at Lord's in 1952.
He missed becoming only the fourth Indian batsman to score hundreds in either innings when he uppishly cut Swann to be caught by a diving Bell at point.
England skipper Kevin Pietersen lauded his team's fighting spirit.
"I'm just really proud to be captain of a bunch of lads who jumped on a plane to come here and played some real good cricket, concentrated so much, they've enjoyed their cricket and have smiles on their faces," he said. "You can't ask for anything more." The visitors resumed their aborted tour after security was assured in the wake of last month's terrorist attacks in Mumbai, the original venue for the second Test.