Wycombe nearly got off to a wonderful start as Gavin Holligan raced clear on 18 seconds to clip the ball over the advancing Steve Phillips only for the ball to bounce wide.
Another great move produced a cross from Holligan that Phillips had to beat away in the seventh minute.
Leading scorer Lee Peacock raced away for City but sent his shot wide of the far post, as the game became very open.
Both sides continued to raid the goalmouths without success, before City were forced to replace Aaron Brown with Joe Burnell on 37 minutes.
City were down to ten men when the captain, Tom Doherty was red-carded for an incident off the ball involving a head-butt to Wanderers' Dannie Bulman.
Wycombe pushed forward and Danny Senda delivered a cross that Holligan flicked past Phillips for a 1-0 lead on 40 minutes.
City brought on Christian Roberts for Lee Miller at the start of the second half and his direct runs and pace caused problems immediately.
However, it was Wycombe who should have gone further ahead when a slick passing movement was spurned as Michael Simpson missed his shot.
Ten-man City were well on top and Wanderers were forced to defend deep.
The entry of Stuart Roberts for Steve Brown brought a second goal for the home side. Roberts drove his shot goalwards; it struck Holligan and flew past Phillips for 2-0 on 68 minutes.
Andy Thomson met a Bulman free-kick on 77 minutes but his free header went straight at Phillips in the City goal.
Roberts came close to getting a goal back when Frank Talia lost his low cross, but there was nobody in the area to take advantage.
It got worse for City when Danny Coles received his marching orders for a second yellow card on 89 minutes, for fouling Jermaine McSporran.
McSporran wrapped up the points for the home side when he cut inside Craig Woodman to fire past the hapless Phillips from 20 yards.