The Middlesex side, who started the weekend bottom of the league, made an imposing 244-4 batting first and then dismissed Bracknell for 234 to leave Ian Caffell's men 30 points from safety.
Wokingham, however, won their first match for over a month as they beat Division One basement side Marlow by 38 runs.
After electing to bat first, Wokingham were dismissed for 198 in the 51st over, with Mark Dozell taking 6-37.
And Dan Reddyhough's men avoided a third straight defeat by bowling out the visitors for 160.
There was also good news for Finchampstead, who eased their relegation worries with an 81-run victory over Amersham.
Dan Marles top scored with 81 as Finch closed on 223-9 before Russell Lane's five-for helped the hosts dismiss Amersham for 142.
In Division 2a, Eversley's title hopes suffered a blow as they were held to an agonising draw by Fleet.
With Simon Mugava scoring 72, Eversley were able to declare after 47 overs with the score at 228-5.
But they still did not have enough time to bowl their Hampshire opponents out as they held on for a draw at 179-9.
Royal Ascot came out on the wrong end of a thrilling encounter against Division 3a leaders Aldershot, eventually losing by just one wicket.
With the Shots in pursuit of just 128 for victory, Ascot looked to be on the brink of causing an upset when they reduced the home side to 89-8.
However, the eighth-wicket pair put on more than 30 runs to frustrate James Summers' men and number 11 Bobby Gill then saw his side home with just two balls to spare.
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