Burns had the ball knocked from his hands when over the line in the Champions Cup clash in October as he paid the price for celebrating a try before it had been scored in a high-profile mistake that went viral and cost his side a win.
But his passage over the whitewash was uninterrupted at the Ricoh Arena as he conjured a superb solo touchdown – his first since the Toulouse calamity – that helped Bath to only a second win in 13 outings.
The former England fly-half also kicked four penalties and a conversion to be named man of the match and propel the club from ninth to sixth in the Premiership.
Wasps were heartened by the return of Dan Robson from the serious ankle injury that ruled him out of England's autumn series, while Brad Shields and Nathan Hughes also made comebacks from their ankle and hip problems.
Robson and Hughes arrived off the bench in the second half and their influence was stamped all over the Wasps fightback that fell short, but it was otherwise a poor afternoon for the Coventry club in front of their second highest crowd of 31,626.
Director of rugby Dai Young stated immediately before the game that "this is going to define our season", but his side now only have one victory in 12 matches yet still remain fourth.
A tense opening half-hour was lit-up by a brilliant try from Burns, who capitalised on Wasps' tight defensive line to dummy Craig Hampson knowing the scrum-half had to cover for a trio of supporting players.
The gap opened up and Burns accelerated through and over the whitewash from 20 yards out to extend Bath's lead to 11-6 after he had landed two earlier penalties.
Hampson invited more pressure on to Wasps when a brainless pass was intercepted by Semesa Rokoduguni and – although the counter was brought to an abrupt halt by referee Matthew Carley, who blew too soon – Nizaam Carr was sin-binned for a high tackle.
Wasps trailed 14-9 at half-time with Billy Searle's three penalties keeping them in touch, but when they spilt the restart and were shoved back at a scrum, their prospects appeared increasingly bleak.
Burns landed another penalty in response to the crumbling set-piece and the same Achilles heal was exposed shortly after, acting as the prelude to a sustained barrage from Bath.
The forwards battered away to gain precious inches and after 19 phases they were over when Will Chudley touched down on the post.
Wasps responded with a well-worked drill at an attacking line-out that saw Thomas Young wheel the driving maul before peeling off and diving over in the right corner.
Nathan Catt had a try disallowed for a double movement but Bath's lead still stood at 10 points and for all Wasps' urgency – now also inspired by the arrival of Lima Sopoaga from the bench – they could not break through.