Hooker Davies finished off a fine attack that began 50m out with a well-worked backs move involving Anthony Allen and Geordan Murphy. Marcos Ayerza and Jordan Crane were also involved before Lewis Moody, on his first start of the season, passed through his legs to find Davies on the left to run in unopposed.
It was his second try in a Tigers shirt after scoring in the corresponding fixture last season. Jeremy Staunton, who had already kicked two penalties, added the conversion.
The home side struck back five minutes before the break through Matt Banahan, the first try Tigers had conceded in 378 minutes since last season’s Guinness Premiership semi-final against Bath.
Fly-half Nicky Little missed the conversion but kicked three penalties to give Bath a slender lead at the break.
Scrum-half James Grindal was making his first appearance for the club since his return to Welford Road this summer. Moody, Julian White and Aaron Mauger made their first starts of the season while Richard Blaze and Jordan Crane were named in the forward pack. Prop Boris Stankovich and centre Dan Hipkiss also returned to take their places among the replacements.
Bath featured two former Tigers, with Peter Short named in the second row and scrum-half Scott Bemand among the replacements. Nick Abendanon was recalled at full-back while Banahan moved to the centre in place of the injured Matt Carraro.