Grimsby Town 1 Doncaster Rovers 0 - Wasteful Doncaster caught on the break
Cook’s 40thinute strike did the damage for Mariners as they shocked Rovers at Blundell Park.
Rovers had plenty of chances to score but squandered them all on what proved to be a frustrating night in front of their 478 travelling fans.
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Hide AdAlex Kiwomya blasted over and so did Ben Whiteman as Rovers made a bright start. Kieran Sadlier had a left-foot shot well-saved by James McKeown and Cameron John rifled wide.
Brad Halliday, Niall Ennis and Sadlier all had good chances as the visitors pushed hard to make their dominance count.
But the home side scored against the run of play after Cook latched on to a pass from Moses Ogbu and slotted clinically into the bottom left-hand corner.
McKeown denied Sadlier with a stunning block a minute later as Rovers came within a whisker of equalising. But Cook was denied on the stroke of half-time by shot-stopper Tim Dieng, who kept his side in the contest with a fine save. Alfie May wasted good chances late on for Rovers as they were left frustrated.
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Hide AdGrimsby: McKeown, Gibson (Hessenthaler 65), Pollock, Davis, Hendrie, Ring (Green 79), Hewitt, Cook, Wright (Cardwell 90), Ogbu, Vernam. Unused substitutes: Russell, McPherson, Hope, Painter.
Doncaster: Dieng, Halliday, James, Anderson, Sadlier, Whiteman (Shead 45), Crawford, Blair (May 79), Kiwomya (Taylor 59), Ennis, John. Unused substitutes: Lawlor, Gomes, Blaney, Longbottom.
Referee: J Brooks (Leicester).