Wasps put their financial woes to one side and held off a Bath comeback to secure their first Premiership win of the season at the Recreation Ground.
Bassett doubled his tally but two tries from Tom Dunn and one from Jonathan Joseph cut the gap to eight points.
Yet Wasps' defence survived the late onslaught for a bonus-point victory.
Wasps travelled to Bath under a dark cloud as owners Wasps Holding Limited filed notice on Wednesday at the High Court over an unpaid tax bill.
Despite saying the move was to give the club more time to find investment, rather than meaning they were in administration, it leaves question marks over Wasps' long-term future.
On the field at least, the visitors had the advantage, having won their last six league meetings with Bath, and they soaked up early pressure to get the first points on the board through two Jacob Umaga penalties.
A trio of tries in seven minutes then opened the floodgates. Bassett tapped down his own chip and Willis added another from close range after intervention from the television match official, while Porter's try stood out for some excellent ball handling in the build-up.
Matt Gallagher - a last-minute injury replacement before kick-off - pulled one back for Bath on half-time but it seemed the same story of old for a winless team who, despite more visits to the Wasps 22, had barely any points to show for it.
Bassett's second pushed the advantage to 29 points however Bath captain Dunn started to turn the tide when he was walked over the line in the pack.
When Willis was sent to the bin for a head collision Bath further capitalised, as Joseph side-stepped under the posts before Dunn set up a nervous finale with his team's fourth of the night to ensure they went away with a point.
Still, it was too little too late as Umaga's fifth penalty ensured Wasps went away with a morale-boosting victory. Bath, meanwhile, are still searching for their first win of Johann van Graan's reign.
'No guarantees on Wasps future'
Wasps' financial plight comes at a time when the Rugby Football Union have also issued a warning to Premiership rivals Worcester Warriors, who face being suspended from all competitions if they cannot provide a "credible" funding plan by Monday.
Wasps' debt relates to £35m in bonds which helped the club finance their relocation from London to Coventry in 2014.
A statement said they were "hopeful of securing a deal" that would secure their future. However head coach Lee Blackett said that while assurances had been given following a meeting with executives Stephen Vaughan, Chris Holland and Derek Richardson, "no-one can guarantee" anything on their future.
"I like what they said, they were honest in their appraisals of where we are. I'm confident that with those guys in place they'll do the right thing for the club and we'll have a club," Blackett told BBC Radio CWR.
As for the approach of his players, Blackett was full of praise for how they approached the fixture with Bath under the circumstances.
"Everyone will take it different ways. I think the majority of players will probably be like me, we have belief that we are going to come out of this.
"Then there will be other players that are probably serial worriers with everything and they'll be worrying about things.
"One thing before the game, as a coach when you've been around the game long enough, when you look in people's eyes you know when they're there and when they're just half there. You knew we were there, there was something going to happen.
"I love Josh Bassett's celebrations in the corner. I only saw them on the big screen out there - but the emotion and how much this club means to him - and he wasn't on his own."
Bath head coach Johann van Graan told BBC Radio Bristol:
"I can look at it two ways - we came here to win, we didn't do that.
"[But] I thought we started the game very well, couldn't score but I'm going to choose to take the positives - that's some fight.
"I saw a real change in attitude and that's what we're going to need more of.
"We've got to go and look from a mental side at minutes 10 to 30, why we struggled."
Bath: Gallagher, Cokanasiga, Joseph, Ojomoh, Muir, Bailey, Schreuder; Boyce, Dunn (capt) Stuart, Attwood, McNally, Reid, Cloete, De Carpentier
Replacements: Doughty, Schoeman, Coetzee, Roux, Van Velze, Green, Francis, Bayliss
Sin bin: Louis Schreuder (41 mins)
Wasps: Umaga, Hougaard, Spink, Odendaal, Bassett, Atkinson, Porter; West, Frost, Alo, Launchbury (capt), McDonald, Carr, J Willis, T Willis
Replacements: Oghre, Hislop, Ryan, Cardall, Morris, Robson, Mills, Kibirige
Sin bin: Jack Willis (60 mins)
Referee: Wayne Barnes