Peter Murphy nodded home the opening goal as the Blues made a stylish start to the game, but City hit back and levelled when David Wheeler converted before the break.
The Grecians then found the winner when Scot Bennett reacted quickest to blast home the rebound after Matt Ingram had parried a header from a free-kick.
Gareth Ainsworth made one change to the side that beat AFC Wimbledon at the weekend, replacing Steven Craig with Max Kretzschmar in attack.
And it was the first chance of the game which brought about the opening goal, with Sam Wood yet again at the heart of the action. The in-form midfielder clipped in an inch-perfect cross which was met with a glancing header by Peter Murphy, who guided the ball into the bottom corner with seven minutes on the clock.
Exeter almost responded immediately when Graham Cummins clipped the outside of the post with a low shot from 20 yards but generally the Blues were in control of the game, winning the ball regularly in midfield and attacking impressively.
They could have doubled their lead when Paul Hayes was sent clear but his low drive was smartly tipped wide by home keeper Christy Pym.
And as the Grecians gradually got a foothold on the game, they also had themselves an equaliser. Graham Cummins surged through on goal and while his shot was parried by Matt Ingram under pressure from Alfie Mawson, David Wheeler was on hand to scramble home the rebound.
Not to be deterred, Wycombe regrouped and almost regained the lead courtesy of a breathtaking move which saw Joe Jacobson set free in the area, and although his shot beat keeper Christy Pym, Scot Bennett was in the right place to clear the ball from two yards out.
It was the visitors playing the more inventive football but the hosts were dangerous with a more direct approach, aided by Jimmy Keohane’s well-timed runs to support Graham Cummins in attack.
By the time the half-time break arrived, City were in the ascendancy but Gareth Ainsworth will have been satisfied with the way his side showed they were able to carve open chances, provided they kept it tight at the other end.
Exeter made a significant tactical switch at the break, moving centre-back Scot Bennett into a forward role prompting a reshuffle which saw Danny Butterfield drop into defence.
The second half began with the same intensity which had made the first half such an entertaining spectacle, and David Wheeler drilled straight at Ingram after Bennett hassled the defence to create the chance.
And Bennett found himself in the right place to hammer home Exeter’s second goal on the hour-mark, hammering home the rebound after Ingram had parried the initial header from Matt Grimes’ dangerous free-kick.
The game started to get away from the visitors and Gareth Ainsworth reacted by introducing Steven Craig and Matt Bloomfield for the bench, replacing Max Kretzschmar and Paris Cowan-Hall.
Bloomfield almost scored with his first touch, receiving Paul Hayes’ pass in space inside the box but the midfielder found himself off balance and drilled over the bar.
Jimmy Keohane headed over from a dinked cross before Matt McClure's low shot was saved by Christy Pym and Steven Craig headed over from a cross from the right.
Three minutes of injury time came and went as City held on nervously for the win, and Wycombe must pick themselves up for the visit of Dagenham & Redbridge on Saturday.
Wycombe: Ingram, Jombati, Jacobson, Mawson, Pierre, Cowan-Hall (Bloomfield 66), Murphy, Scowen, Wood, Kretzschmar (Craig 66), Hayes (McClure 80).
Unused subs: Richardson, Rowe, Lewis, Walker.
Exeter: Pym, Ribeiro, Woodman, Oakley, Bennett, Davies, Butterfield, Wheeler (Noble 80), Grimes, Keohane, Cummins (Nichols 90).
Unused subs: Hamon, Riley-Lowe, Tillson, Jay, Watkins.
Attendance: 3,129 (192 from Wycombe)