David Villa had seen a 16th-minute penalty saved by Keylor Navas, and that looked like it would prove a costly miss as Barca - perhaps with one eye on Tuesday's Champions League semi-final first leg against Bayern Munich - struggled to break down a spirited Levante defence before Fabregas' late breakthrough.
The win left Barcelona 13 points clear of second-placed Madrid, who beat Real Betis 3-1 earlier on Saturday evening to briefly reduce the gap, and meant Tito Vilanova's side could win the title next weekend.
Full-back Eric Abidal made his first start for Barca since February 2012, having undergone liver surgery last year, and looked an assured presence throughout the 90 minutes.
Andres Iniesta and David Villa also returned to Vilanova's line-up. Star man Lionel Messi returned to training on Friday after a thigh injury but was not risked on the bench ahead of Tuesday's trip to Germany.
Navas started between the posts for Levante ahead of regular number one Gustavo Munua, and managed to frustrate Barcelona for much of the match.
He got down well in the 13th minute to keep out a close-range attempt from Thiago and three minutes later made an even more noteworthy contribution.
The hosts were awarded a controversial penalty when David Navarro was adjudged to have fouled Iniesta as he looked to work his magic down the left. The visitors were clearly aggrieved and will have felt justice was done when Villa's spot-kick was kept out by Navas, with Fabregas' follow-up deflected over the bar.
Iniesta engineered a shooting opportunity from the edge of the box on 25 minutes but Navas was not unduly troubled.
Cristian Tello sidefooted a volley into the side-netting just after the half-hour as Barca continued to push for the opener.
Villa attempted to make amends for his penalty miss with a fierce effort in the 40th minute, which was bravely blocked by the head of Juanfran.
Navas scrambled to his right to keep out another deflected blast Villa three minutes later as the game reached the interval goalless.
The second half continued in much the same vein, with Barca bossing the possession but unable to find the necessary spark in the final third.
Vilanova brought on Xavi, Pedro and Alexis Sanchez during the second half, and the latter played a key part in setting up the game's only goal six minutes from time.
After provided a deflected cross for Villa which the Spain striker half-volleyed over the bar in the 81st minute, the Chile forward caused Levante problems down the right again three minutes later. He produced the perfect pass for Fabregas, who showed neat control and despatched a fine shot into the bottom-left corner.
Buoyed by the goal, Barca could have added to their lead in the closing stages. Fabregas again saw a powerful drive parried by Navas and then Pedro was denied after latching onto the rebound.
There were no further goals, but the hosts had done enough for the win that moved them one step closer to to regaining the La Liga crown and will send them to Bavaria in good spirits.