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In the day's other early match French giants Perpignan were being held 14-14 by Italian outfit Treviso 18 minutes from the final whistle before romping away to a 35-14 win.
Wasps, who drafted in French veteran flank Serge Betsen and made him captain as a late injury replacement, seized control of the match early on against a Glasgow side who had come into the game full of confidence after ending a 12 year drought in winning their first match of the campaign against the Dragons.
However, they were on the back foot from the start as the hosts scored their first try through 22-year-old scrum-half Joe Simpson, who squirreled down the blindside and touched down in the corner.
Flyhalf Dave Walder failed to convert but after missing a penalty he found his touch and converted two penalties with the only response from the Scots a penalty by Ruaridh Jackson.
The game was really up for the visitors - who have just one win on the road in European Cup play though it was against Toulouse in 2008 - when prop Moray Low was sin-binned in the 24th minute.
Wasps didn't waste any time in making them pay as Walder's expertly angled grubber kick into the right hand corner was gathered by wing Tom Varndell who had not trouble touching down with the Wasps flyhalf then adding the conversion from the right hand touchline.
Though Glasgow refused to surrender limply, Jackson having a splendid individual match as he scored 19 of their points including a try, there was never any danger of the visitors improving Scottish sides woeful record against English opposition which stands at just 12 wins in 57 matches with just two of those in England.
Toulouse top ther Pool 6 after easily beating the Dragons on Saturday.
Perpignan like Wasps came into their match on the back of an opening defeat against Llanelli Scarlets in Wales last weekend and for a while it looked as if Treviso were going to push them as hard as they did two-time winners Leicester in their opening match.
However, the match ended as a contest when the referee awarded Perpignan a penalty try 18 minutes from time after the Italian scrum had been warned about intentionally bringing it to the ground.
The Italians' heads went down after that and the hosts ran in two further tries, the fifth and last one by Chouly a superb move begun inside their own half and which travelled through four players hands.
Perpignan manager Jacques Brunel was delighted to have got a victory on the board.
"These five points (they got an offensive bonus point) have re-energised us totally," he said.
"We are not dead, we are alive. Now qualifying will be played out in December when we play Leicester. We can still believe (in reaching the last eight)."
Leicester later took control of Pool 5, their five second half tries lifting them to a 46-10 bonus point win over Llanelli at Welford Road.
Llanelli's Morgan Stoddart got the first try of the game, with Stephen Jones adding the conversion and a penalty but it was the hosts who led 13-10 at half-time thanks to a Martin Castrogiovanni touchdown and eight points from Toby Flood.
The Scarlets were then steamrollered aside in the second half with tries from Ben Youngs, Thomas Waldrom and Tom Croft (2) and Matty Smith.
In France, Biarritz maintained their unbeaten start in Pool 4 with a 35-15 bonus points win over Ulster, with last season's finalists' scrumhalf Dimitri Yachvili responsible for 15 of Biarritz's points.
Takudzwa Ngwenya grabbed two second half-tries and Manuel Carizza and Sylvain Marconnet also crossed to seal maximum points for the French outfit - Andrew Trimble and Stephen Ferris produced late scores for Ulster.
