Plunkett's maiden Test 50 helped England to 319 all out early on day three, despite Bhuvneshwar Kumar's six for 82.
Then, after the hosts had eked out a 24-run lead in this second Investec Test, the pace-bowling all-rounder took two big wickets in two balls.
In sunshine instead of the forecast rain, India eventually closed on 169 for four thanks to an ultra-patient four-hour half-century from opener Murali Vijay (59no).
England now have a feasible chase over the last two days for a first win in 10 Tests, but it took until early evening before England's bowlers made much progress, with only the wicket of Shikhar Dhawan to show for their efforts in 43 overs.
Plunkett then not only broke a second-wicket stand of 78, having Cheteshwar Pujara caught-behind, but took another prize victim as Virat Kohli left a delivery which kept coming up the slope and hit the top of off-stump.
When Stuart Broad had first-innings centurion Ajinkya Rahane controversially caught-behind shortly after, England had three wickets for five runs.
Plunkett's 55no in 75 balls followed his promotion to number seven as nightwatchman the night before. He and Matt Prior defied the best overhead bowling conditions of the match, completing a handy 51-run stand.
Plunkett was more worried about England getting their noses in front than his half-century
"I was just trying to get past that lead, that was more important, but it's nice to get that first Test 50 and I'm absolutely over the moon with it," he said.
"I've been working hard. I've felt good with the bat all year and I've been working on some stuff, and last night when I came in as nightwatchman I worked really hard on lining it up and I felt in good nick and came out this morning a little bit more confident."
Ben Stokes continued his unenviable sequence of three successive ducks for England, bowled trying to drive Kumar.
Broad counted four between gully and point first ball, but edged his second to Dhawan at slip as Kumar got his fifth and sixth wickets in the same over.
The seamer's instant follow-up was a perfect way to celebrate his place on the Lord's honours board, but he got no change out of number 11 James Anderson.
Doubtless still on a high from his world-record batting heroics and career-best at Trent Bridge, Anderson had the confidence to smack his second ball past cover for four to end an eventful over.
He stuck at it to make 19 of the 39 he and Plunkett added for the last wicket before gloving an attempted reverse-sweep at Ravindra Jadeja into the hands of slip.
India's openers were unscathed for 15 minutes before lunch, and only Dhawan succumbed in the afternoon - cutting Stokes fiercely to point where Joe Root took an outstanding catch.
Dhawan's opening partner Vijay was notably unworried as Alastair Cook ran through his bowling options, and Pujara was studied too. Their slow grind frustrated England until Plunkett's sudden intervention.
Broad then found enough bounce to hit Rahane on the arm-guard, umpire Bruce Oxenford probably thinking it was the bat handle as he gave the unfortunate batsman out after Prior scampered round to leg-gully to make a low gather.
At 123 for four, India appeared vulnerable, but Vijay completed his painstaking 162-ball 50 with successive boundaries off Anderson in an unbroken stand of 46 with a very determined Mahendra Singh Dhoni.
Plunkett added: "I think tomorrow we'll come out hard again … I think the wicket's only going to get better so we'll go hard in the morning and see what happens."