The hosts were put into bat after losing the toss and suffered an early blow as Charlie Thurston fell for a second ball duck.
In-form opener George Thurstance (15) followed shortly after and when Nick Barden was out for 28, Beds were 63-3.
However, skipper James Middlebrook, back from his Yorkshire duties, then put together a match-winning 77-run partnership with Andy Reynoldson.
Middlebrook was dismissed for 49 from 28 balls, with two fours and four sixes, while Reynoldson passed his half century, run out for 54 in the final over.
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Ed Wharton came into smash the last ball of the innings for a maximum as Beds ended on 162-5.
The hosts attack set about their task well, as former Northants batsman Ben Howgego fell for five, bowled by Andy Nunn.
Reynoldson and Wharton then took over, as Reynoldson claimed superb figures of 3-27, while Wharton took 2-16 from his four overs, as Cambs were reduced 64-6.
Colin Griggs got in on the act, to finish with 1-8 from three miserly overs, while although there was an eighth wicket partnership of 27, once Lewis Bruce was caught by Reynoldson off the bowling of Nunn (2-24) the fight was over.
Beds eventually restricted Cambs to 120-8 as they fell 42 runs short.
Beds are now back in MCCA Unicorns Championship Eastern Division action this weekend as they visit third placed Buckinghamshire.
The match takes place at Burnham CC and starts on Sunday, ending on Tuesday evening.
Beds are sitting sixth in the table after two games, with both matches finishing in high-scoring draws.