England declared on 333 for seven late in the middle session, with Gary Ballance’s fourth Test century the cornerstone of a superb third innings effort.
Anderson, on the occasion of his 100th Test, took the new ball on 382 Test scalps, just one behind the milestone set by Sir Ian Botham 23 years ago.
He was handed two overs before tea without success, but Broad did get England’s victory push moving when he bounced out Kraigg Brathwaite with his fifth delivery.
Ballance had earlier laid the foundations with a fine 250-ball stay containing 11 fours and two sixes.
The 25-year-old had a torrid World Cup but picked up where he left off in the longer format, having scored three hundreds last summer.
England were thoroughly professional in setting up the game, resuming on 116 for three and adding 217 in 48 overs, a run-rate of just over 4.5.
Ballance was assisted in no small part by selflessly attacking efforts from Joe Root (59), Ben Stokes (35) and Jos Buttler (59no).
Buttler, in particular, sparkled at the crease.
He was at the crease for just 56 deliveries but struck five boundaries and two mighty sixes as he showcased much of his thrilling repertoire.
He swept and reverse swept with wonderful timing off the spinners and hit long and hard down the ground.
Had England not declared to give themselves five overs before tea, he would surely have done even more damage to West Indian spirits.
With all eyes on Anderson and his imminent place in the record books, Broad set the ball rolling for the tourists.
As in the first innings he made the new cherry spit at the batsman’s body, a proposition Brathwaite was unable to deal with.
He fended skittishly to Root at short leg and the hosts went to the interval in trouble on nine for one.
The expectation on Anderson was palpable, but with the ball refusing to swing he was made to work hard for any rewards.
There were gasps of excitement at every half chance but nothing concrete in his first five overs.
Darren Bravo nudged one in front of short leg then sprayed airily in the region of Chris Jordan at gully, but neither were particularly close to finding hands.
Anderson and the close catchers went up in unison when he rapped Devon Smith on the pad but it was a shout in hope rather than expectation.
Captain Alastair Cook gave his main man plenty of time to get the job done, extending his opening burst to seven overs but it ended wicketless.
The last ball of his spell was another lbw appeal against Bravo, Anderson giving a lung-busting cry, but umpire Billy Bowden spied a thin edge.
And with that, it was over to Broad.