There seemed little danger when, in the 27th minute, the home side lofted a high ball into the Chesterfield box, but John Sutton nodded down for strike partner McLeish to smash a stunning 25-yard volley past Spireites keeper Barry Roche for his 17th goal of the season.
The goal came after both sides had missed chances to take the lead. Firstly, Wycombe midfielder Tommy Doherty chested down a cleared corner and his rasping right-foot volley was tipped over by Chesterfield keeper Roche.
Then visitors forward Jamie Ward forced home keeper Frank Fielding into a terrific one-handed save after racing on to a Jamie Lowry through ball.
McGleish broke the deadlock soon after, which seemed to galvanise the hosts and from another corner, full-back Russell Martin rifled in a right-footed drive that Roche could only parry into the path of Leon Johnson, but his follow-up was cleared off the line by Janos Kovacs as Wycombe ended the half firmly on top.
The trend continued after the break and Doherty should have put the home side further ahead after Sergio Torres' pass found him in space, but he curled his shot inches over when it looked easier to score.
Matt Bloomfield then saw his header from a substitute Leon Knight's cross saved on the line by Roche.
Then a superb move between Bloomfield, Doherty and Torres saw the latter swing a lovely ball onto the head of Knight, but his close-range header looped just over.
Chesterfield's only response came from substitute Steve Fletcher, who fired a snap shot straight at Fielding and Ward, who volleyed tamely over when well placed.