Although the defeat does not topple Bracknell from the summit of South West One East, they are now heading a pack of four teams with six wins from their opening seven matches.
Closest to the Lily Hill men are newly-promoted Centralians, who went into the weekend on the back of five successive victories.
Not since their clash with Reading on the first day of the season had Cents tasted defeat, but they fell behind inside five minutes at Lily Hill Park.
With the pitch soaked from a heavy downpour and both teams preferring to kick early on, it was Bracknell who came up trumps first.
A cross-field kick bounced perfectly for winger Ian Burch to collect and score near the uprights, Ceri Cummings adding the extras for 7-0.
Cents hit back with a penalty from Liam Hemming but Bracknell extended their lead with a couple of three-pointers from Cummings.
The 10-point advantage didn't last long as full-back Lewis May kicked on an up and under, won the race with the defence and then dived on the ball over the line.
Hemming converted to close the deficit further and Cents then held firm to deny Bracknell inside the 22.
The home side saw a couple of driving mauls stopped and were then pushed off a scrum under the posts before Cents cleared their lines with a penalty.
Another penalty before the interval, this time inside Bracknell territory, was then kicked by Hemming to make it 13-13 at the break.
Bracknell started the second half brightly but were unable to add to their tally as knock-ons disrupted their attacks in the face
of Cents' unwavering defence.
Hemming kicked the visitors into the lead for the first time with his third penalty and Bracknell then turned down the chance to level the scores with a three-pointer from in front of the posts.
Instead they decided to run the ball, but were again held up by Celts and failed to add to their tally.
The home side continued to pile on the pressure in the closing stages but a drop goal from Hemming edged Cents further in front and they held on to their six-point advantage.
Bracknell will be looking to bounce back when they go to local rivals Reading on Saturday (3pm ko).