Centre Sofiane Guitoune scored two tries for Toulouse, including a clincher 17 minutes from time, while wing Medard also touched down and full-back Thomas Ramos kicked two conversions and a penalty.

Burns and centre Jamie Roberts looked to have sent Bath on their way with first-half tries.

But Wales international Roberts did not appear for the second period after being on the receiving end of a Jerome Kaino tackle that saw the New Zealand World Cup winner sin-binned, and Bath missed his physical presence.

Despite Burns adding 10 points from the boot, four-time European champions Toulouse capitalised on his profligacy, and closed the game out to leave Bath already facing a mountain to climb in terms of any quarter-final aspirations.

Roberts returned to Bath’s starting line-up after recovering from a cheekbone injury, but his international colleague Taulupe Faletau was sidelined with a broken arm and England prospect Zach Mercer replaced him at number eight.

Burns kicked Bath into a third-minute lead, but Toulouse responded impressively, driving play upfield through their heavy duty ball-carriers and then allowing Ramos, centre Maxime Mermoz and scrum-half Sebastien Bezy to unsettle Bath’s defence.

And the home side could not hold out as Toulouse’s forwards took charge and lock Iosefa Tekori gave an unmarked Medard an easy finish, with Ramos’ conversion making it 7-3.

Bath were guilty of some straightforward handling mistakes, which helped Toulouse gained a degree of territorial control, yet when they produced error-free rugby it reaped a try-scoring reward.

Lock Dave Attwood smashed his through the first wave of Toulouse defenders to set up a gilt-edged attacking opportunity, and Bath did not waste it as flanker Francois Louw supported strongly before giving Roberts a scoring pass.

Burns converted, and Bath struck again five minutes later, adding a second try after impressive work by captain Rhys Priestland and centre Jackson Willison, with Burns applying a superb one-handed finish before kicking a touchline conversion that put his team 10 points clear.

Toulouse, though, were dangerous on the counter-attack and they trimmed Bath’s lead as the interval approached when fly-half Zack Holmes moved possession wide and Guitoune sprinted clear to level the try count.

But Toulouse ended the half a player short when Kaino was yellow-carded by referee Andrew Brace for an illegal tackle on Roberts, only for Burns to miss two penalty chances that would have given Bath more breathing space.

Roberts went off for assessment, but he did not rejoin the action, returning to tske a seat on the touchline as the second half began with Burns rediscovering his range by kicking another penalty for a 20-12 lead.

Ramos reduced the arrears when he kicked a penalty Bath flanker Tom Ellis was sin-binned for a dangerous tackle, and then Guitoune rounded off patient approach work before Ramos’ conversion edged Toulouse home, assisted hugely by Burns’ agony.

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