Bath were pushed hard by Championship side Cornish Pirates as they won 29-23 in the opening round of fixtures in the Premiership Rugby Cup in Penzance.
Fly-half George Worboys scored 14 points as a young Bath side scored four tries to go top of Pool C.
The revamped event features sides from the top two tiers of English rugby.
Meanwhile, in the evening's other tie, Championship newcomers Cambridge conceded six tries as they were beaten 38-11 at Doncaster Knights.
Pirates impressed in the first half against their top-flight opponents as Ben Grubb blasted through two tackles to cross the Bath try-line to put the hosts 11-7 up, after Ewan Richards had scored for the visitors.
John Stewart was forced over from a line-out maul a couple of minutes from half-time to put Bath 15-11 ahead at the break.
Pirates' scrum was impressive but Worboys got an impressive third try 12 minutes into the second period before Will Trewin pulled a try back for the hosts, as he did well to get on the end of Iwan Jenkins' kick with 12 minutes to go.
But Sam Harris secured a bonus point for Bath as he went over with five minutes left, before Kyle Moyle got on the end of a speculative kick in the 78th minute to set up a tense finish as Bath held on and the Pirates secured a losing bonus point.
At Castle Park Cambridge briefly led as Steffan James' two penalties put the National One winners 6-5 up after George Simpson's try.
But tries from Maliq Holden and Rhys Tait in the final five minutes of the first half saw the Knights lead 19-6 at the break.
AJ Cant scored twice in four minutes early in the second period as Doncaster stretched their lead to 31-6, before Cambridge hooker Morgan Veness pulled a try back with 20 minutes to go after Holden was sin-binned.
Holden returned to get his second try with eight minutes left after Seb Nagle-Taylor's break, as the Knights top Pool D - which also includes Bristol, Northampton and Ealing.