New Zealand, overnight 199-3, went to lunch on 225-5 with a lead of 54 after scoring just 26 runs in 26 overs.
Nightwatchman Neil Wagner batted throughout the morning session to move from 4 to 13, facing 100 balls in two hours at Sir Vivian Richards Stadium. Dean Brownlie was unbeaten on 5.
Roach, who has 3-47, dismissed Taylor lbw for 21 to a delivery that angled in. In his next over, Roach struck the off stump of Williamson (0) with a devastating leg-cutter.