Defender Leon Johnson saw red early on for Wycombe.
First-half goals from Chris Atkinson - on his debut following his loan move from Huddersfield - and Jack Lester were answered by a Neal Trotman own goal before Sam Hird made the points safe late on.
Wycombe had to reorganise after 10 minutes when Johnson was sent off for pulling down Marc Richards with the striker through on goal, and they were behind four minutes later.
The visitors failed to cut out a cross from the right and Atkinson smashed a right-foot shot past Nikki Bull at his near post.
Chesterfield doubled their lead in the 20th minute when a 25-yard volley from Sam Togwell was diverted past Bull from eight yards by Lester and only a mis-kick by Drew Talbot saved Wycombe from going three behind in the 35th minute.
Joel Grant fired inches over for the visitors in the 65th minute, but Wycombe were back in it seven minutes later when Trotman tried to clear a corner only for the ball to go in off his shin. Any chance of a comeback was ended in the 85th minute when Hird headed in a free-kick.