Fabregas put the Gunners on their way with a 72nd minute opener, before Hleb popped up in second-half stoppage time to double the advantage.
The 20-year-old midfielder coolly side-footed home from the edge of the penalty area after Gael Clichy had won the ball in the Sparta half and jinked his way past two defenders.
Then, with the full-time whistle just seconds away, Bacary Sagna latched onto a quick throw out from Jens Lehmann and sprinted down the left flank before squaring the ball for Hleb who scuffed a low shot beyond Tomas Postulka in the home goal.
Arsene Wenger had named the same starting line-up that opened their new Premier League campaign with a 2-1 victory over Fulham at the weekend.
But it was Sparta who started brightly and carved out the best openings of a first half in which both sides were guilty of committing a number of rash challenges.
Jan Rezek was denied by a combination of Lehmann and the post when the German keeper deflected his low drive onto the woodwork in the ninth minute.
At the other end, Fabregas tried his luck with a 20-yard drive which Postulka turned away.
Lehmann then came to Arsenal's rescue for the second time late in the half when he dived bravely at the feet of Rezek to snuff out a dangerous break.
Libor Dosek was next to try his luck when he glanced a header wide on the stroke of half-time as the home side looked to press home their advantage.
Arsenal gradually played their way back into the game in the early stages of the second half but, for all the midfield probing of Tomas Rosicky and Hleb, the visitors struggled to play lone striker Robin van Persie into the match.
The Netherlands international went close with a low shot across goal before almost forcing an own goal in the 64th minute when he whipped over a dangerous cross that deflected off a defender and narrowly avoided nestling inside the far post.
But Fabregas and Hleb were in the right place at the right time to slot home decisive away goals and move the Gunners close to the lucrative group stages of Europe's premier club competition.