England, at lunch on the fourth day, were 129 for one in their second innings - still 154 runs short of avoiding an innings defeat with the three-match series level after the drawn opener at Lord's.
Strauss was 54 not out and Vaughan, who during his innings became the 17th England batsman to score 5,000 Test runs, 36 not out.
Their stand so far was worth 80.
But the session was marred by the lastest of several unpleasant incidents this series when India fast bowler Shanthakumaran Sreesanth brushed shoulders with Vaughan and was spoken to by South African umpire Ian Howell.
England resumed on 43 without loss, with Strauss 21 not out and fellow left-handed opener Alastair Cook unbeaten on 17.
But to the 14th ball of the day Cook, on 23, was leg before for the fourth time this series, left-arm quick Zaheer Khan the successful bowler on Monday, and England were 49 for one.
Khan then produced a superb delivery to Vaughan, on nought, that just missed the off stump after jagging back in.
It was impressive bowling from Khan whose first innings figures of four for 59 played a major part in England being bowled out for a meagre 198.
Sreesanth, India's quickest bowler, also posed problems before he over-stepped the mark in his confrontation with Vaughan.
It was a sign of the increasing tension between the two sides which on Saturday saw Khan take exception to a comment from the England slip cordon and brandish his bat in their direction before the umpires stepped in to calm the situation.
England initially found runs hard to come by on Monday but Strauss broke the shackles by pulling and extra-cover driving left-arm quick Rudra Pratap Singh for two fours in as many balls. Meanwhile Vaughan went runless for 26 balls until driving medium-pacer Sourav Ganguly for four.
Singh was convinced he had Vaughan, on 11, caught behind by wicket-keeper Mahendra Singh Dhoni. But replays suggested Australian umpire Simon Taufel had been right to reject the appeal with Vaughan's bat appearing to hit the ground, not the ball.
Vaughan, seemingly unflustered, then elegantly drove Ganguly straight down the ground but on 16, to leg-spinner Anil Kumble's first delivery of the day, survived a well-merited lbw appeal with the ball hitting pad first.
Strauss, who pulled a full toss from occasional leg-spinner Sachin Tendulkar to go to 49 with his fifth four, then completed a 120-ball fifty.
India's first innings total of 481 saw five members of their top six score fifties with Tendulkar leading the way with 91. During his innings Tendulkar became only the third batsman in history to score 11,000 Test runs.
Brief Scores (at lunch, D-4):
England 198 and 129 for 1 (Strauss 54 n o, Vaughan 36 n o, Cook 23; Zaheer 1 for 23) Vs India Ist innings 481 (Tendulkar 91, Ganguly 79, Karthik 77, Jaffer 62, Laxman 54; Panesar 1 for 101, Tremlett 3 for 80).