McClure followed up his brace in the midweek League Two win at Rotherham with another two strikes against the Brewers, who had captain Zander Diamond sent off at Adams Park on Saturday.
Wycombe took the lead inside 13 minutes when McClure followed up after Joel Grant's shot was parried by Dean Lyness to squeeze the ball in. Bruno Andrade almost doubled the Chairboys' advantage when his effort from the edge of the area came off the outside of Lyness' near post.
Wycombe keeper Jordan Archer was then forced into his first difficult save when he pushed away Billy Kee's half-volley.
The hosts doubled their lead in the 57th minute after they were given a penalty when Zander Diamond hauled down McClure and was shown a red card.
Grant held his nerve from the spot to send Lyness the wrong way and McClure made the result safe by slamming in a rebound after Andrade had been denied.