West Indies had kept a tight rein on their hosts through the first two sessions at Old Trafford but leaked runs after tea to hand England the upper hand in the decisive test.
Pope offered one catching chance and survived two reviews as he played a positive innings to enhance his growing reputation.
He was nine runs short of his test century when he took the offer of bad light.
Buttler, whose place in the team is under threat after a poor run with the bat, played a supporting role in the unbroken 136-run partnership. He took 104 balls to reach his half century and was 56 not out at the close.
Rory Burns also contributed 57 runs before being caught at first slip by an instinctive grab from slip fielder Rakheem Cornwall, one of the highlights of the day for the West Indies.
West Indies captain Jason Holder won the toss and put his bowlers back to work at the start of their third test in a matter of 16 days.
It looked the right decision after Dom Sibley went without scoring in the first over of the day and England's danger men Joe Root and Ben Stokes made negligible contributions.
Root was run out for 17 and Stokes bowled for 20 by Kemar Roach, the pick of the bowlers who ended the day with figures of 2-56 off 18.4 overs.
Stokes looked uncomfortable at the crease as he struggled with a quadriceps strain, picked up during his second test heroics, and was cleverly set up by Roach, who after two bouncers produced a perfect in-swinging delivery to strike down the stumps.
England sacrificed a batsman to include an extra seamer in their line up because of the likelihood that Stokes will not be able to make of a contribution with the ball.
The series is tied at 1-1.