First half goals from Ed Upson and Sam Foley ensured Gary Johnson's side avoided an upset against the League Two Chairboys, who had Matt Spring sent off in the first half.
The Glovers started the game brightly, with Byron Webster, James Hayter and Upson all spurning early chances.
Wycombe midfielder Spring was shown a straight red card from referee Gavin Ward in the 27th minute after a reckless challenge on Gavin Williams.
Five minutes later, the dominant League One side took a deserved lead when Korey Smith's dinked cross was headed home by Upson.
The advantage was doubled on the stroke of half time when Foley slammed home from six yards after a headed knockdown by Joe Edwards.
Depleted Wycombe, who came into the game on the back of three straight league victories, came close to scoring through Dean Morgan and Matt McClure after the break, but the Somerset side held out to keep their Wembley dream alive.