Centre-back Dave Walton, back in the starting line-up following a five-week injury lay-off, gave the home side a first-half lead, while two second-half goals from Darren Moss and one from Duane Darby, enabled Shrewsbury to run out comfortable winners, with a last minute consolation from substitute Efe Echanomi all Orient could muster.
During the past month Shrewsbury's concerns have been about the other end of the table as they have hovered just above over the relegation zone and following last Saturday's home defeat against Wycombe, manager Gary Peters recalled Walton and striker Darby to his side, with both decisions paying dividends.
There had been little to enthuse over in the opening 40 minutes as both teams struggled to keep possession, but the deadlock was finally broken four minutes before the break when Walton rose at the far post to give Town the lead with his second goal of the season.
Six minutes after the break and just 60 seconds after former Gay Meadow man Lee Steele wasted an excellent opportunity to put the visitors level Shrewsbury extended their lead when Darby bundled the ball over the line from close range after Luke Rodgers had fired across goal.
In the 68th minute Moss blasted home his first of the afternoon and Shrewsbury's third with a well-struck drive from 15 yards and when he headed home a Sam Aiston centre on 75 minutes, his fourth goal of the campaign made him Shrewsbury's leading scorer.
Echanomi's last-minute effort just ensured an exact reversal of the scoreline when the teams met at Brisbane Road last October.