After earlier collapsing to 298, despite resuming on 268 for four, England recovered with the wickets of Dinesh Karthik, captain Rahul Dravid, Tendulkar and Jaffer to limit India to 145 for four at stumps. The tourists still trail by 153 runs.
Sourav Ganguly is 25 not out and was joined by nightwatchman Rudra Pratap Singh (five).
Ganguly, who made 136 on his Test debut at Lord's 11 years ago, might have also perished when he cut Chris Tremlett through gully for four as Ian Bell failed to take a difficult chance.
The day began three hours late because of rain after an admirable effort by groundstaff following a monsoon-like deluge. The patient crowd was compensated for the loss with an exciting spectacle as 10 wickets fell on the day.
India began shakily as Karthik succumbed for five when Ryan Sidebottom had him lbw and Dravid edged James Anderson to Matt Prior after the wicketkeeper earlier dropped a straightforward chance from Jaffer when he was on nought.
The fall of Tendulkar, though, after his 79-run stand with Jaffer, created the usual animated celebration that routinely greets his dismissal.
He was out for 37 after playing a loose stroke to a ball from Anderson that came into him, rather than the usual away-swinger.
Tendulkar, who embarked on his first Test tour of England in 1990, is still without a Test or one-day international century at Lord's.
Howevr, he did surpass Steve Waugh's tally of 10,927 Test runs to become the third-highest run scorer, trailing only Brian Lara (11,912) and Allan Border (11,174), who have retired.
Jaffer fell shortly before stumps on 58 after offering a return diving catch off a short ball from six-foot-seven debutant Tremlett.
England needed the breakthroughs after losing their last six wickets for 26 runs. It was a far cry from Thursday evening when they were 219 for one with Strauss (96) and Michael Vaughan (79) well set.
The most dramatic moment of the collapse was Kevin Pietersen's dismissal that was eventually not given and then his genuine departure, both occurring when he was on 37.
Pietersen edged Zaheer Khan to wicketkeeper Mahendra Singh Dhoni, who claimed the catch and the batsman subsequently began to walk towards the pavilion.
When the big screen showing the replay proved the ball had bounced, while the umpires waited for the third umpire's adjudication, Pietersen wandered back and was reprieved. He fell to the same combination in the next over though.
Shanthakumaran Sreesanth trapped three of England's tail-enders lbw to finish with three for 67.
India are seeking their first Test series win in England since 1986.