England openers Rory Burns and Joe Denly survived four overs of their second innings before lunch, scoring nine runs without loss, leaving the visitors 110 runs behind at the break.
It was a good morning for England, who wrapped up the four outstanding West Indies wickets for only 34 runs.
Bravo was the last man out, stumped off Moeen Ali for 50. He faced 216 balls in a marathon stay at the crease, stroking two boundaries.
Tailender Alzarri Joseph scored seven, hours after the death of his mother, who reportedly had been in ill health for some time.
Stuart Broad (3-53) was the pick of the England bowlers on Friday but his teammates got in on the action on Saturday, with James Anderson collecting the wickets of Jason Holder (22) and Kemar Roach (6), while Stokes dismissed Joseph.
With the pitch still offering the pace bowlers some assistance, a draw seems unlikely with two full days and two sessions remaining. West Indies lead the three-test series 1-0.