City have now recorded maximum points from their last two games while Barnet have only won once in their last six.
Barnet had the game's first chance when the trickery of Richard Graham on the left wing ended with a low teasing cross which Lee Roach met, but keeper Chris Porter made a vital block.
City took some time to create any sort of opening, but from Darren Dunning's free-kick on 25 minutes Paul Groves flicked the ball goalwards and Shane Gore saved well at the near post.
Barnet were not allowed to settle in possession and from some sustained City pressure Donovan, revelling in his new central midfield role, ran at the visitors defence and his goalbound shot was deflected for a corner.
The visitors then went close when two City defenders missed a free-kick launched down the middle and Giuliano Grazioli's flick struck the outside of the post.
Just a minute before the interval, City went ahead. Paul Robinson and Andy Bishop linked on the edge of the box and released Donovan, whose right-foot angled shot from eight yards beat Gore at his near post.
In stoppage time Dave Merris made a vital clearance in clearing a wicked inswinging Barnet corner off the line.
Barnet equalised on 58 minutes when Dwane Lee took a ball launched over the City defence in his stride before firing in a low cross which Grazioli stabbed home from close range.
Defender Jon Maloney was desperately unlucky to see a venomous volley pushed over the bar by keeper Gore from Groves' flick.
From the well worked resulting corner Dunning's pin-point curling cross was knocked home by Maloney from six yards.
City defended stoutly to repel the expected Bees response, while near the end both Bishop and Merris went close to adding a third.