However, assistant coach Jordi Roura is not entertaining any thoughts of wrapping up the title despite watching his side move one step closer to doing just that, after Fabregas' 84th-minute winner handed them all three points against the Granotes.
Although second place Real Madrid kept pace with a 3-1 win over Real Betis, Barca can win the title next weekend should they beat Athletic Bilbao and their rivals lose in the Madrid derby to Atletico Madrid.
And Fabregas was happy his side managed to pick up the win on Saturday despite the distraction of a UEFA Champions League semi-final first leg against Bayern Munich on Tuesday evening.
"The title is close," he said after the game. "It was important to win, even though some people want to make out that the league doesn't matter.
"Obviously we had to try to forget about the Bayern game tonight [Saturday], but it's always much better going into the Champions League having won matches like these."
The ex-Arsenal captain also believes the hard-fought triumph against Levante will stand his team-mates in good stead ahead of what is expected to be a thrilling European last-four clash the Bundesliga champions.
"We're happy to have prepared for Tuesday's game like this," Fabregas added. "It was tough to play against a defence like Levante's.
"It was a tough game. There was a long stretch in the first half in which we weren't very good but we were better in the second."
But despite Fabregas' enthusiasm as the Catalans edge closer to replacing Real as champions of Spain, Roura is staying grounded.
"We'll go to Bilbao and try to win the game," Roura said on www.fcbarcelona.com. "We will take this one game at a time. The sooner we can win the title, the better.
"There's no doubt that there's a lot of merit in winning four out of the last five editions of the competition - if we win this year. This is a very difficult tournament."
He added: "This Saturday we suffered quite a bit to win the game. This points to how hard the competition is and it gives value to the fact that we've won 84 points so far and that we have such a big advantage over one of the best Real Madrid sides ever.
"It's normal to have ups and downs. Perhaps we were lacking fluidity but that was largely due to how well Levante played.
"There is nothing that could overshadow our joy if we win La Liga."
Roura praised Eric Abidal after the defender's assured performance in his first start for Barcelona in over a year helped move the Catalan club to the brink of the Primera Division title.
"This is a very happy day for everyone," Roura said when asked about the Frenchman's performance on his first Barca start since February 2012 following liver surgery last year.
"He played the entire match and he feels great. On a footballing level, I think he played well. He paced himself perfectly.
"We have to enjoy this moment. We will have time to sit down and talk about his contract extension before the season is over. The important thing is that he played the whole game."
Alexis Sanchez's future has been the subject of much speculation lately, with Juventus and Inter Milan reportedly interested in trying to lure him away from Barca this summer.
But the Chile forward, who set up the winning goal for Fabregas after being introduced as a 77th-minute replacement for Cristian Tello, remained focused on the task in hand when asked about his future last night.
After pointing out that his contract runs through to 2016, Alexis said his objective - at least this term - was "to win La Liga and the Champions League".
He added: "If the manager needs me, I'll be 100 per cent ready. I'm improving on a daily basis and I'm fitting in with the team."