Anderson, playing his first Test since January's final Ashes clash in Sydney and his first at home since 2004, led the way as India were bowled out for 201 to give England a first innings lead of 97.
Left-armer Ryan Sidebottom followed up with four for for 65 as the two seamers, in the absence of injured quicks Matthew Hoggard, Stephen Harmison and Andrew Flintoff, got England back into the match after the hosts had collapsed to 298 all out.
At lunch, England were eight without loss in their second innings, a lead of 105. Andrew Strauss was nought not out and fellow left-hander Alastair Cook unbeaten on eight.
Anderson, whose previous Test best of five for 73 also came at Lord's, during his debut match against Zimbabwe in 2003, added Sourav Ganguly to a list of wickets that already included fellow star batsmen Rahul Dravid, the India captain, and Sachin Tendulkar.
India resumed on 145 for four with Ganguly - who scored a hundred at Lord's in his Test debut 11 years ago - 25 not out and nightwatchman RP Singh unbeaten on five.
Ganguly though was clean bowled for 34 by an Anderson delivery that swung back into the left-hander in Saturday's sixth over to leave India 155 for five.
Meanwhile debutant quick Chris Tremlett, who shortly before the second day's collected his first Test wicket when he caught and bowled top-scorer Wasim Jaffer for 58, after the opener had been put down on nought by wicket-keeper Matt Prior, continued to bowl with good pace and aggression.
Anderson, after a fine spell of one wicket for two runs in four overs, was replaced by Sidebottom.
And with his fifth ball Sidebottom had Singh skying to Anderson at mid-off for a Test-best 17.
Singh's exit brought in hard-hitting wicket-keeper Mahendra Singh Dhoni.
However, a ball after hesistantly guiding Anderson just short of the slips, he was out for nought when a similar shot carried to Ian Bell at third slip to give the 24-year-old Lancashire quick his fourth wicket of the innings.
Sidebottom followed up with an inswinger that saw Anil Kumble lbw for 11 before having VVS Laxman caught behind.
Anderson ended the innings when Zaheer Khan miscued a hook to Strauss at first slip to finish with excellent figures of five for 42 in 24.2 overs in the opening match of a three-Test series.
It was the third time he'd taken five wickets in an innings in his 17-Test career but the first since his debut season.