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India were 142 for four at lunch, needing 316 more runs to reach what would be a new record victory target of 458.
No side has made more in the fourth innings to win a Test than the West Indies' 418 for seven against Australia in Antigua in 2002-03.
Tendulkar, bidding for his 100th international hundred on a ground where his Test-best is 37, was seven not out and Suresh Raina four not out after India lost Rahul Dravid, Venkatsai Laxman and Gautam Gambhir in the first session.
India resumed on 80 for one, with Dravid 34 not out and Laxman 32 not out after Matt Prior's unbeaten 103 on Sunday had rescued England from the depths of 62 for five.
Dravid had added just one run to his overnight total when he inside-edged fast bowler Chris Tremlett onto his pad with a leaping Ian Bell at short leg unable to hold the tough one-handed chance.
Fortunately for England, Dravid was out for 36 when James Anderson made him play away from his body and edge to wicketkeeper Prior.
Dravid, who had scored an unbeaten century in the first innings, swished his bat in annoyance and India were 94 for two.
Laxman, in trademark style, flicked Broad of his legs for a boundary to complete a 104-ball fifty featuring eight fours.
But he gave his wicket away on 56 when he pulled Anderson straight to Bell at mid-wicket.
The 38-year-old Tendulkar, in what could be his last Test innings at Lord's walked out to a standing ovation, having been prevented from batting in his usual No 4 spot because he had been off the field for two sessions Sunday with a viral infection.
The 'Little Master' got off the mark with a four clipped off Anderson.
But at the other end Gambhir, batting with an elbow injury, was lbw to off-spinner Graeme Swann for 22.
India, who had lost two wickets for four runs in eight balls, were now 135 for four.
The excitement generated by the climax to this match, the 2 000th Test of all-time and the 100th between England and India, was evident from the capacity 28 500 crowd, many of whom had been in lengthy queues around Lord's before play got underway.
