The Dons were way below-par and, despite going close through Keith Andrews and Jemal Johnson in the second half, just could not find an equaliser.
Their lead at the top now been reduced to eight points.
The visitors totally outclassed the Dons in the first half and could have gone in to the interval with a bigger lead.
From the start they looked dangerous and had the first effort on goal on nine minutes when Cliff Akurang's 25-yard shot fizzed wide.
Ashley Carew had a superb chance to open the scoring on 18 minutes but just volleyed wide after a cross from Jason Puncheon had dropped at his feet.
But Carew was not to rue his miss too much as Barnet did open the scoring four minutes later.
Puncheon's dangerous cross missed everyone but fell perfectly to Yakubu at the back post who tapped in from point-blank range.
But there was controversy straight afterwards as lineswoman Amy Raynor put her flag up, then immediately down. The Dons substitutes remonstrated with her, but the goal stood.
It took the Dons nearly half-an-hour to register their first shot but Andrews' 25-yard shot was well-saved.
Carew should have punished the Dons when Dean Lewington gave the ball to him just outside the box, but he shot too early and the ball flew wide.
And then, on the stroke of half-time, Andrews had another effort which summed up their performance, his 30-yard free-kick going absolutely miles over.
The Dons kept Barnet penned in their own half after the break and had an early chance but a combination of Rob Beckwith and Joe Devera kept out Johnson when he was through on goal.
From the resulting corner Sean O'Hanlon somehow headed over from point-blank range.
They did not create another chance until the 71st minute, but it was a glorious one.
Luke Howell's cross found Andrews unmarked but, from ten yards out, he headed wide.
They continued to huff and puff, and in the last minute should have scored when Drissa Diallo's cross-cum-shot was just tipped wide and substitute Aaron Wilbraham somehow headed into the side-netting.