Adam May scored the only goal of the match as the U's now sit on 48 points while the Dons remain in the relegation zone, one point from safety.
Story of the game
AFC Wimbledon should have taken the lead four minutes later. Sam Cosgrove got on the end of a through ball, but the ball ran away from him and although it fell to Osew, Paul Digby was on hand to clear.
The U's then broke the deadlock almost immediately out of the halftime break. Joe Ironside's back-pass found May and his strike into the top corner from 25 yards out gave Tzanev no chance.
Sam Smith could have doubled the visitors' lead as he met a chipped cross in the box, but his header was just inches wide. At the other end, Cosgrove shot into the stands from a wonderful position.
Cambridge had a chance to double their advantage in the 69th minute, a cross by Harrison Dunk finding Smith at close range, but Ben Heneghan stuck a boot out to avert the danger.
Wimbledon were desperate for an equaliser, a free kick straight into the wall and a corner punched away by Mitov. A penalty shout was also waved away in the 82nd minute.
Despite seven minutes of stoppage time, the hosts could do nothing and Cambridge all but ensured their safety for next season.
Man of the match: Adam May
He scored the goal that likely kept Cambridge in League One and had other chances to add to his tally as well as setting up his teammates. Overall, a solid performance.