Rangers fan Cook lashed home his second of the season 18 minutes into the game to ease the pressure on Ian Holloway, who was given the dreaded vote of confidence from his chairman earlier in the week.
The winger's strike was a rare piece of quality as both teams played like they'd rather have been watching Celebrity Big Brother than playing a game of football.
Jamie Cureton cheekily back-heeled to his strike partner Paul Furlong, who in turn offloaded for Cook who blasted home at the near post from 18 yards.
And he could have had a second just after the break when Steve Simonsen spilled the midfielder's strike just wide of his own net.
Gareth Ainsworth should have put daylight between the sides on 52 minutes when he raced up the right wing to shoot just wide of the far post from a tight angle.
Cureton then set up Furlong midway through the second half for a header from close range, which drew a good save from Simonsen.
Rangers, who last won back in November against Cardiff, boasted Middlesbrough defender Andrew Davies and Charlton keeper Simon Royce - both signed on a month's loan - as part of a new-look back-line.
But just as Davies looked to be slotting into the back four perfectly, he was forced off at the break with an injury.
After the controversy of the fixture at Britannia Stadium earlier this season, in which Gerry Taggart accused QPR midfielder Marc Bircham of play-acting to get him sent off, there was little to write home about for much of the first half.
Stoke, who fielded the same team that performed so well against Arsenal in the FA Cup last weekend, failed to register a single shot on target for the entire first half, with Chris Greenacre coming closest with a shot high over the bar.
Greenacre produced Stoke's first attack of the second half on the hour, but he was thwarted in the area by Davies' replacement Matthew Rose.
John Eustace headed the ball home from Carl Asaba's cross in the closing stages, but the offside flag denied the Potters an equaliser.