Wing Christian Wade scored two of Wasps' tries, while number eight Nathan Hughes and replacement Guy Thompson were also on the scoreboard, with fly-half Andy Goode booting 12 points with three conversions and two penalties.
Wasps had to contend with a spirited fightback from the Cherry and Whites, who were well down at one stage.
Their tries came from full-back Rob Cook, who touched down twice, prop Shaun Knight and number eight Sione Kalamafoni, with fly-half Freddie Burns adding two penalties and two conversions.
They were firmly on the back foot for the opening 20 minutes as Wasps turned up the heat.
The Londoners showed their intent with a seven-minute burst of action inside home territory when a Goode kick to the Wasps try area just ran dead before wing Elliot Daly could touch down.
But Wasps were not to be denied and soon Wade scored a superb try as lock Tom Palmer laid off a pass just over halfway for the wing to breeze past defenders Rob Cook and Tom Savage and go over for a converted touchdown.
Just minutes later, Wasps stung the Cherry and Whites again. Their pack dominated the home scrum inside the 22 and, when big back row Hughes picked up 10 metres from the line, he skipped past a limp attempted tackle from centre Henry Trinder to bound over.
It put Wasps firmly in the driving seat at 14-0 ahead but Gloucester grew into the game thereafter.
The Cherry and Whites spent a good five minutes in the Wasps 22 and just on the half-hour, they finally got their reward when Burns booted a straight-forward 23-metre penalty in front of the posts.
And the home team narrowed the deficit even further when Knight pounced on a loose ball for a try which Burns converted superbly from the touchline.
But Wasps had the last laugh before they went into the break as Goode struck home a 24-metre penalty to put his side 17-10 ahead at the break.
Gloucester hit back within minutes of the re-start when they played a trump card at an attacking line-out, hooker Huia Edmonds throwing quickly to Kalamafoni at the front to dive in from 10 metres.
Wasps were suddenly struggling to get any ball to get into the game as the tables were well and truly turned. Indeed, locks Palmer and Kearnan Myall double-teamed brilliantly to deny centre Ryan Mills a certain third home touchdown.
Eventually, Gloucester took the lead for the first time when Burns landed a 23-metre penalty but that was quickly eradicated by a long-range Goode penalty.
The final quarter was frantic as Cook scored the first of his two tries but Thompson went over at the other end after a terrible mistake from home scrum-half Jimmy Cowan let Bassett in to feed the replacement.
And Wasps' victory was assured by the terrific 50-metre score down the right by Wade, who outpaced all the cover to score.
Cook's second try in the dying seconds at least gave the Cherry and Whites something from the game rather than nothing they looked likely to finish with.
- Sports & Recreation
- Freddie Burns
- Andy Goode