Shrewsbury did their League One survival prospects no good as they slumped to their sixth home defeat of the season.
Salop boss Graham Turner rang the changes with the fit-again Jon Taylor reintroduced along with Luke Summerfield, Chris Porter and Yado Mambo.
But there was not enough attacking threat to worry the Londoners who won comfortably with goals in each half, the second a penalty needlessly conceded by David McAllister.
Mathieu Baudry headed Dean Cox's cross into the far corner after 33 minutes.
And when McAllister dived in on Romaine Vincelot, Kevin Lisbie sent Chris Weale the wrong way from 12 yards six minutes into the second-half.