The seamer, who overtook Ian Botham to become the country’s leading Test wicket-taker in the drawn first Test in Antigua, bowled Kraigg Braithwaite with his seventh ball of the contest after England won the toss and chose to bowl.
Devon Smith (15) was likewise unable to see out the session, although replays suggested he hit the ground rather than edged Chris Jordan behind ??? the curious dismissal ensuring that the West Indies went into lunch on 36-2.
Earlier, showers ensured that play started 105 minutes late in testing conditions for batting after Cook had called correctly.
The tourists made just one change to their XI, recalling Moeen Ali at the expense of James Tredwell who was declared fit to play despite a recent arm injury.
West Indies made two changes, bringing in leg-spinner Devendra Bishoo for Sulieman Ben,n but more tellingly calling up Shannon Gabriel in place of fast bowler Jerome Taylor, ruled out with a shoulder injury.
Anderson began the session with 384 victims but quickly added another, knocking over Braithwaite with the first ball of his second over after opening the Test with an over of outswing.
The Lancashire seamer found prodigious movement to bowl Braithwaite through the gate, the opener ??? who had already nicked a chance short of slip – losing his balance badly.
England???s slip cordon learned little from Braithwaite???s earlier let-off and a second chance when begging in the seventh over, Darren Bravo edging Anderson just short of Ben Stokes.
Stuart Broad struggled for accuracy in his opening spell and despite only conceding eight runs off his five overs was the first to be replaced by Chris Jordan.
Nine balls into his spell Jordan came close to removing Devon Smith but Gary Ballance was unable to hold the sharp chance at leg-slip.
Jordan didn???t have to wait long for recompense, although Smith initially stood his ground after being given caught behind ??? and, as replays showed, with some justification as his bat hit the pitch rather than the ball.
His failure to review the decision tilted the session firmly in England???s favour, with Jordan taking lunch with figures of 1-8 off two overs.