The usually free-scoring Bees had struggled to find a way past United goalkeeper Matt Glennon who was in fine form.
They had trailed for the majority of the match, but after Carlisle had Tom Cowan and Danny Livesey sent off in the 70th minute, Barnet were able to press forward and capitalise.
Carlisle looked to have soured the taste of champagne until Grazioli somehow managed to turn the ball past Glennon in a crowded penalty area with the last kick of the match.
Magno Vieria had given Carlisle the lead in the 31st minute when he capitalised on an error by Ismail Yakubu.
The Brazilian-born striker was first to react after the Barnet centre-back only half cleared Chris Lumsdon's through ball. Vieria picked up the loose ball before lashing it past Scott Tynan in the Bees net from 25 yards.
Lumsdon thought that he had increased United's lead five minutes later when his free-kick appeared to be goalbound. But as the midfielder threw his arms in the air to celebrate, Yakubu somehow made amends for his earlier error by hacking the ball off the line.
Ironically it was the Bees who had started the better. Grazioli should have give the champions the lead in only the eighth minute but he failed to connect with Ben Strevens' tempting cross.
Richard Graham then burst into the Carlisle box before feeding Dean Sinclair but the ball got stuck under the midfielder's feet and when he did manage to muster a shot at goal it was easily saved by Glennon.
Carlisle looked to add to their tally in the second half with Peter Murphy going close.
But their chances of winning the match were handed a severe blow when Cowen received his marching orders after handling Yakubu's goalbound header.
Referee Mr Lee awarded a spot-kick that Simon Clist sent blazing over the bar.
After the miss Livesey continued to protest with Mr Lee who wasted no time in flashing the red card for the second time.
Barnet threw everything forward with Dean Sinclair and Nick Bailey going closest before Grazioli kick-started the celebrations which sent boss Paul Fairclough running on to the pitch in delight.