An early try from South African wing Sam Gerber handed the hosts a nightmare start in High Wycombe and they trailed 10-6 as a result at the half-time break.
But Wasps put a stuttering first 40 minutes behind them as they hit back with a brace of quick-fire tries after the interval.
Blindside flanker Ed Jackson and wing Josh Bassett touched down after 52 and 55 minutes respectively as the Wasps pack began to assert their authority on a hugely physical Bayonne eight.
"We are pleased with the result and very happy with the response in that second half. Getting two wins under our belts early on definitely gives you more confidence in your group and so we will leave happy tonight," said Young.
"The first half was disappointing and the players felt they let themselves down in that 40 minutes. We had a bit of a rallying cry at halftime in the changing room.
"We talked about how we'd lost the ball far too often and how we were allowing their pack far too much ball. We clawed our way back into it and I was very pleased with the response.
"The forwards were really good again and in that second half they did a good job at sapping the energy out of that heavy Bayonne pack. We are getting better and better as a pack but we know there are bigger challenges to come."
Next up for Wasps in the Amlin Challenge Cup is the December double header with Grenoble, starting with the away leg at the Stade Lesdiguières.
Young's men know they will be top of the table by at least four points heading into that first trip to France as Grenoble left last week's away game at Bayonne empty handed.