For their victory they can thank an excellent performance from Davies, who not only marshalled his forwards but also laid the foundations for plenty of good work from Henry Paul and Keil outside him in the centre.
But it was the Gloucester forwards who really stood out. Against a pack boasting Leo Cullen, James Hamilton, Will Skinner, Henry Tuilagi and Michael Holford, the likes of the outstanding Terry Sigley, Jack Forster, Mark Cornwell, Will Matthews and number eight Mark George kept them in check throughout.
For Sigley and Cornwell, it was their second game in 48 hours following their contributions against Bucuresti on Saturday but both did the home pack proud.
Gloucester dominated the scrums and recovered from the early loss of loose-head prop Kevin Moran with a broken arm to hit back after Leicester started with a flash.
They were 10-3 ahead as early as the sixth minute when Alex Dodge cut a mazy angled run past Kyle Palm and Bailey to score next to the posts following a period of concerted pressure.
Davies cut the gap with a penalty but it was the Tigers who dominated early on. Gloucester needed a way into the game somehow and it came when Davies read a pass between Tom Youngs and Matt Cornwell in midfield to surge home from half-way and score beneath the posts.
Sigley was already on the field at this stage and after 30 minutes Gloucester scored again. Paul was involved twice in a move alongside Quinton Davids and when possession came right, Ali James fed Bailey on an overlap and the full-back put Gloucester 18-10 ahead.
And six minutes later, Gloucester were in again. Again it was Davies who made the initial break before James Merriman cut a superb angle through a crowd of defenders before delivering his pass perfectly for Bailey to score.
Ian Humphreys landed a penalty before the break but Gloucester had established a comfortable 25-13 lead. The second period failed to live up to the first and was scoreless until the final 10 minutes.
Gloucester were still on top but neither team retained possession long enough to become truly effective. However, Keil marked his debut with a try when Paul fed him a lovely little pass from 10 metres close to the posts.
However, it was the young Leicester side who finished the stronger. When they kept possession they caused Gloucester some problems and the hard working Cornwell was rewarded for his efforts with a try that cut the gap to 32-20.