The Windies reduced England to 122-4 after Jason Holder won the toss, Kemar Roach the standout bowler with 2-56 in Manchester on Friday (July 24).
Pope (91 not out) and the under-pressure Buttler (56no) raised their bats for the first time in the series, an unbroken stand of 136 taking Joe Root’s side on 258-4 when stumps were drawn 15 minutes early due to bad light.
Rory Burns earlier made 57 at the top of the order before he was superbly caught by all-rounder Rahkeem Cornwall, playing his first match of the series.
England moved Ben Stokes up to number four and picked a five-strong bowling attack, including Jofra Archer and James Anderson, so the Windies will be disappointed not to have made further inroads but weather could prevent either side from forcing a win.
Roach snared Dom Sibley, a centurion in England’s victory at the same venue last week, leg before without scoring from the final ball of the first over but the Windies suffered a blow when an injured Shannon Gabriel left the field.
England were 66-2 at lunch after captain Joe Root (19) was brilliantly run out by a direct hit from the alert Roston Chase after paceman Gabriel was able to return.
Roach produced a peach of a delivery to clean up Stokes, Man of the Match in the second Test following two magnificent knocks, for 20 prior to Burns bringing up a patient 126-ball half-century.
Cornwall then took centre stage to see the back of Burns with a brilliant one-handed reaction grab for at first slip off the bowling of Chase, leaving England four down before tea.
The classy Pope looked anything but a man out of touch with the Windies bowlers looking weary, finding the rope with a flurry of glorious drives and bringing up his 50 off 77 balls.
Buttler was watchful before dispatching spinner Cornwall for two sixes in an over and also reached his half-century, with West Indies unable to strike with the new ball.
Roach closes in on double-century
Roach was the pick of the Windies bowlers and conjured up a special delivery to see the back of the in-form Stokes, who made a hundred and a rapid half-century to set up a series-levelling win last week.
The Barbados-born fast bowler made a great start by trapping Sibley in front and then got one to nip back in and bowl Stokes, the newly-crowned top-ranked Test all-rounder, through the gate for his 199th scalp in the longest format.
Cornwall makes his presence felt
Cornwall had to be patient to get his chance to play a part in the series and although he was wicket-less, the sizeable all-rounder certainly made an impact on the first day of his third Test.
The 6ft 6in tall, 22 stone Antiguan, selected instead of Alzarri Joseph, snaffled a sharp chance to get rid of Burns and generated turn without reward.
Pope and Buttler to the rescue
England were in danger of being dismissed cheaply when Buttler joined Pope at the crease, only for the fifth-wicket pairing to turn the tide.
Pope has been out of sorts in the series, but returned to form in style with elegant strokes on both sides of the wicket and Buttler offered great support with a timely knock with his place under threat.
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