Malan was not out at 28 with 4 boundaries and Cook was at 153 with 23 boundaries at the time of the close of Day 1.
Joe Root, the England captain, called a halt after former skipper Alastair Cook was out for 243 in the first day/night Test staged in Britain.
Root, in keeping with a remarkable run of form that has now carried him to half-centuries in each of his last 11 Tests - a new England record that he brought up with a rare loose shot outside off against Jason Holder - was, as usual, the principle aggressor.
Former England captain Alastair Cook recorded the fourth double century of his Test career and James Anderson struck an early blow to the West Indies' faint hopes of a recovery before inclement weather brought a premature end to day two of the inaugural day-night Test match held on United Kingdom soil.
The West Indies lost Kraigg Brathwaite before the tea break with the opener's footwork letting him down as he prodded at a full ball outside off from James Anderson.
That left the West Indies with a tricky nine overs to bat in twilight before the tea interval. With Cook's wicket falling, England declared the innings with 514 for 8.
Joe Root entered Test cricket's courageous new world with a familiar onslaught of old-school run-harvesting, as he and his senior statesman, Alastair Cook, made light of another flimsy top-order showing from their new boys to rack up an imposing 176-run stand that has already spanned the best part of three-and-a-half hours.
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Together with Root (136), he put on 248 for the third wicket.
"We didn't have too many preconceived ideas, went in with an open mind and tried to just play the situation in front of us, so I thought we did very well today".
His pull off Miguel Cummins, one of four seamers in the attack, saw Malan complete a 112 ball-fifty.
The landmark was reached in a way that rather epitomised the Windies' misery when Cook slashed a single to third man, only for Hope to comically trip over his own feet and allow the ball to trickle to the boundary.
Cook was 213 not out at lunch.
WEST INDIES: K.C. Brathwaite, K.O.A. Powell, K.A. Hope, S.D. Hope, R.L. Chase, J. Blackwood, S.O. Dowrich, J.O. Holder, K.A.J.
Westley was also out cheaply as he was trapped lbw on review after missing a straight ball.
If Cook's methods were once again a case of substance counting more than style, there was much to admire from his more aesthetic fellow left-hander who unfurled a succession of cover-driven boundaries between bouts of hard-working defence.
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