The fly-half pulled the strings all afternoon, setting up Wade's try in the first half and then keeping the visitors at bay with two drop goals in the second half.
This was only Wasps second win in their last 13 Aviva Premiership fixtures but against an under-strength Leicester they impressed in windy conditions.
Owen Williams slotted four penalties for the visitors, who had 13 players out injured while Dan Cole, Toby Flood, Geoff Parling, and Ben and Tom Youngs were all retained by the England squad.
The Welshman, making his first Aviva Premiership start, was off target with two long-range penalties in the first five minutes as Tigers made most of the early running.
But with their first opportunity of the match it was Wasps who struck first, thanks in no small part to the quick thinking of former Tiger Goode.
The fly-half took a quick tap from a free-kick and burst through the middle of an unsuspecting Tigers pack to set up field position deep in the 22.
And when the ball was spread right skipper Chris Bell floated a lovely pass with his left hand out to Wade and the winger had the simplest of tasks to dot down.
Goode added the extras from wide out but the seven point lead did not last long, Williams finding his range from much closer in with a penalty to make it 7-3.
The rest of the half saw Goode and Williams trade penalties as both sides struggled to make an impression with ball in hand and the sides went in at the interval with Wasps 13-9 to the good.
It was the Tigers that made the brighter start to the second half and Carlo Festuccia was sent to the sin bin for the hosts as Wasps continued to infringe in their own 22.
Those 10 minutes with the Italian in the bin were spent almost entirely with Tigers on the front foot but Wasps defended manfully and actually extended their lead thanks to the opportunism of Goode.
The fly-half slotted a drop goal in the 52nd minute after a rare Wasps foray into the Leicester half.
And two minutes later Goode was clearly starting to enjoy himself as he repeated the trick, this time from further out, to put Wasps 19-9 ahead as Festuccia returned.
As the game ticked past the hour mark Tigers began to chase the game and a few errors crept in as a result.
But Goode was off target with a long-range penalty that could have punished the Tigers and the visitors came roaring back.
First Williams slotted his fourth penalty of the game in the 68th minute to make it 19-12 and get the Tigers in position to claim a losing bonus point.
But the reigning champions wanted more than that from the game and pushed hard without ever really looking like finding the try that would level the scores.
And the game was up in the 76th minute when Goode slotted his third penalty of the night for a 17-point total and to deny his former employers a losing bonus point.