With regular strikers Giuliano Grazioli and Liam Hatch missing through injury, the Bees found an able deputy in Lee Roach whose 39th minute goal seemed enough to maintain their relentless march towards the Conference title.
But Burton never gave up the fight and their determination was rewarded when Stride grabbed the equaliser in the third minute of stoppage time.
The Brewers made a lively start, winning three corners in the first two minutes, but the Bees soaked up the pressure with relative ease.
Chris Hall twice fired wide from the edge of the area and Stride had a header comfortably saved by Scott Tynan.
The visitors gradually began to seize control of the game, though their goal came as something of gift.
Burton brought back reinforcements to defend a Simon Clist corner, but the ball sailed over a cluster of heads and Roach pounced for a close-range finish.
Burton twice went close to the equaliser in a flurry of pressure at the start of the second half, Aaron Webster lashing a 20-yard free kick a fraction too high and Craig Dudley dipping a 25-yard effort on to the roof of the net.
But Barnet looked increasingly menacing on the break and had chances to seal a comfortable victory.
Nicky Bailey burst on to a Richard Graham pass to thump a post from 25 yards in the 55th minute and Ben Strevens spurned a gilt-edged chance when he jabbed a Bailey free-kick wide from four yards in the 66th minute.
Then a swift counter attack by the visitors ended with Damien Batt skimming the crossbar with a 20-yard shot.
But Burton's never-say-die spirit drove them forward for final assault and it paid dividends as Stride notched his first Conference goal of the season.
Barnet failed to clear a long throw-in by Webster and the ball broke loose for the Burton skipper to rifle home a left-foot shot from 10 yards.