The home side came into Friday's clash having learned that flanker Marcell Coetzee will be out for another nine months after returning to South Africa to have further surgery on a serious knee injury.
Wasps are injury-ravaged themselves with director of rugby Dai Young complaining of having to open their European campaign just five days after defeat to Saracens in the Premiership, while Ulster enjoyed an extra 48 hours' rest following their Pro14 win over Connacht last weekend.
And Young's mood will hardly have been improved by seeing hooker Tom Cruse (thumb) and centre Brendan Macken (head) depart the action inside 20 minutes.
Wasps did lead 6-3 at the break thanks to the boot of Jimmy Gopperth, who added a further three points early in the second period, before Ulster finally found their feet in slippery conditions.
Christian Lealiifano went agonisingly close to the opening try as he came up just short, but Ulster did not have to wait long as wonderful work from Charles Piutau in the 55th minute sucked in Christian Wade and Willie le Roux, allowing Jacob Stockdale to score in the left corner.
That same pair combined again two minutes later, Piutau breaking to feed Stockdale, who threw over his head and back inside for Stuart McCloskey to go over.
John Cooney missed both conversions but it mattered not as Lealiifano slotted two penalties in the final 10 minutes - the second after Josh Bassett was sin-binned for a high shot - as Ulster ensured Wasps left a sodden Belfast without so much as a losing bonus point.
FULL TIME: Tries from Jacob Stockdale & Stuart McCloskey help @UlsterRugby to turnaround their half-time deficit at the Kingspan Stadium pic.twitter.com/26gndTsXzG
— Champions Cup (@ChampionsCup) October 13, 2017
Photo by Getty Images. Caption: Christian Lealiifano in action for Ulster v Wasps