Set the improbable target of 628 to win, or more hopefully required to bat two days to save the match, the tourists lost four wickets in the middle period of the day to limp to tea at 217 for six.
Chase, who ended opening batsman Rory Burns' quest for a maiden Test century off the final delivery in the morning period of play, was persisted with by captain Jason Holder for the next two hours and earned the reward of the wickets of England skipper Joe Root, Ben Stokes and Moeen Ali.