England dominated for much of the day and, after the Windies had slipped to 139-7 in the afternoon, James Anderson returned to complete a fine bowling display.
Leading by 68 between innings, England were on the back foot quickly as Taylor trapped Jonathan Trott (9) to pile more pressure on the batsman, whose future has been the subject of much debate since his return to the side.
It was soon 18-3 when Taylor hit the pads of Ian Bell's (0), and a foolish review from England's number four was further proof of the desperation which had crept into the innings.
Ali (8) joined Gary Ballance at the crease, but England were dealt another blow with five minutes left in the day when the all-rounder dragged on while playing a risky cut shot to give Permaul his first wicket of the innings.
Ballance (12*) and Ben Stokes (0*) managed to survive until the end of play, and England's hopes of regaining control at the Kensington Oval could come down to their partnership as they look to add to their 107-run lead tomorrow.