At tea West Indies were 153 for three with Devon Smith on 40 and Shivnarine Chanderpaul, returning after missing the second Test defeat because of injury, on 15. Harmison had taken two for 39 from nine overs.
England were dismissed shortly before lunch for 370 with Ian Bell falling three short of what would have been a seventh Test century.
Harmison struggled with his line and forced wicketkeeper Matt Prior into several diving stops to prevent four byes down the leg side. He still produced enough good balls to remind the batsmen of his 11 wickets on the same ground last year against Pakistan.
He followed his first wicket of West Indies stand-in captain Daren Ganga (5) before lunch with a good short delivery to remove Runako Morton for 35 from 39 balls, a straightforward catch to Andrew Strauss at first slip.
Morton, who made a career best 201 in a tour game this week, had shown his aggressive intentions by striking left-arm spinner Monty Panesar for two sixes. Morton's stand of 67 with Smith came off just 81 balls.
In between those dismissals, Liam Plunkett had dangerous left-hander Chris Gayle caught at backward point by Alastair Cook for 23 off a casual, poorly executed drive.
Smith, on seven, survived a scare when his edge off Plunkett narrowly evaded the hands of first slip Strauss at head-height.
England are 1-0 up in the four-match series and seeking to close out the series before the fourth match starts next Friday at Durham.
Match referee Alan Hurst dismissed an official complaint by West Indies team manager Michael Findlay about England's bowlers contravening the laws by practising near to the playing surface during a break in play.
Brief Scores (at tea, D-2):
England Ist innings 370 Vs West Indies 153 for 3 (Davon Smith 40 n o, Runako Morton 35; Harmison 2 for 39, Plunkett 1 for 18).