England had reduced the visitors to 145 for seven on a bowler-friendly pitch early in the final session, but Rahane's 103, along with support from number nine Bhuvneshwar Kumar (36), ensured India had rallied to 290 for nine at the close.
Having won the toss and elected to bowl, the hosts initially struggled to find their rhythm on a green-looking surface, taking only two wickets before lunch.
However, a four-wicket burst in the middle session followed by another dismissal shortly after tea put England in control before Rahane's late assault. Rahane's knock, which included 15 fours and a six, was ended by a sharp caught-and-bowled effort by James Anderson late in the day.
Tail-enders Ishant Sharma (12) and Mohammed Shami (14) safely navigated the closing overs, helped by field placings that at times saw five or six fielders on the boundary, to ensure England will have to come out and bowl on Friday morning.
"I just wanted to be myself and play my game, I was just talking to myself, I wanted to play as close (to my body) as possible and play my shots," Rahane told a news conference.
"First session they bowled a little bit short and second session they came with a different plan and (pitched) a little bit up.
"That sort of line on this wicket will suit our bowlers as well. Tomorrow is going to be a crucial day... it's not going to be easy for the English batsman either."
The Lord's surface was in marked contrast to the one used in Nottingham, which came in for fierce criticism for its placid nature as the first match of the five-test series petered out to a tame draw.
After being presented with a pitch to their liking, England initially failed to grasp the opportunity to make significant inroads into the Indian line-up, with openers Shikhar Dhawan (7) and Murali Vijay (24) the only wickets to fall before lunch.
However, four more dismissals in the middle session put the hosts in the driving seat.
Anderson had the dangerous Virat Kohli caught by Matt Prior for 25, the wicketkeeper looking slightly sheepish after dropping two catches before lunch, while Ben Stokes knocked back Cheteshwar Pujara's middle stump after an obdurate 28 from 117 balls.
Captain Mahendra Singh Dhoni, who raised England's ire after Anderson was reported for an incident involving Ravindra Jadeja at Trent Bridge, received a frosty reception from the Lord's crowd and much to their delight, lasted only 17 balls before being caught by Prior off Stuart Broad for one.
Jadeja, also unpopular with the home fans, was trapped lbw by Moeen Ali for three, leaving India in disarray at 128 for six before the tea interval.
Stuart Binny (9) was also out leg before, although had the decision review system been in use the decision may have been overturned as Anderson's delivery appeared to be going over the wickets.
However, Rahane, in his seventh test, took advantage of England's tiring bowling attack and brought up his second test century with a stab through to the offside boundary off Anderson.
He put on 90 with Kumar before the latter, who passed 50 in both innings at Trent Bridge, was bowled by Broad soon after the new ball was taken.
The 31-year-old Anderson's four-wicket haul made him England's most successful wicket taker on home soil, surpassing Fred Trueman's tally of 229, and he also eclipsed Ian Botham (69) by becoming the highest test wicket taker at Lord's with 72 victims.
"I think there is a bit of frustration, especially the last session there with the tail hanging around with Rahane, but you've got to give credit to him, the way he played," all-rounder Ben Stokes said.
"It was a really good knock.
"But from a positive side, we had them 140 for seven, taking away from today is that we keep knocking their top order over."
He also paid tribute to Anderson, who did not let a misconduct charge that could rule him out for up to four tests distract him.
"Watching him bowl you just feel like he's going to nick someone off or, next best, play and miss. He swings the ball both ways, a very skilful bowler and you've got him holding an end up all the time."