Francois Wiese scored a try double as he helped Bicester win 26-21 at Drifters in Southern Counties North on Saturday.
Ryan Gallagher and Dan Spencer also crossed over for the improving visitors, who have now lost just once in five matches.
Spencer also kicked three conversions for the visitors.
On Saturday, Bicester entertain High Wycombe.
Alchester slipped to the bottom after losing 21-16 at Milton Keynes.
Saturday’s opponents, who were deducted five points earlier in the season, head them by virtue of games won.
Alchester led 16-15 with ten minutes to go, but Milton Keynes won it with a late try.
The visitors were awarded a penalty try after Milton Keynes collapsed three successive scrums.
Tom Miles converted this and three penalties.
Alchester are without a game this weekend.
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules hereComments are closed on this article