Fabregas started up front in the absence of the injured Lionel Messi and made a welcome return to form as he also played a part in Barca's other two goals, scored by Alexis Sanchez, as the Catalans restored their 13-point lead at the top of the table.
However, the biggest cheer of the night was reserved for Eric Abidal as he made his first appearance in 14 months after undergoing a liver transplant.
The Frenchman replaced Gerard Pique with 21 minutes remaining to a rapturous reception from the Camp Nou crowd and coped comfortably with Mallorca's limited threat going forward.
Afterwards Abidal wanted to thank his cousin who was his donor for the transplant just over a year ago.
"Thank you to my cousin, without whom I wouldn't be here today," he told Canal+.
"Thank you for all the support to my family, my friends and all the supporters of FC Barcelona.
"I would also like to say thank you to all the people in the hospital that have fought what I have fought.
"Today has been a special day and I remember all those who are fighting like I was in the hospital."
Any doubts over whether Barca would be able to cope without Messi against the league's bottom side were quickly dispelled by two goals in a two-minute spell midway through the first-half.
A lovely one-two between Alexis and Fabregas played in the latter to open the scoring before the Chilean made it 2-0 after Dudu Aouate had parried Fabregas' shot.
The same two players combined for another two goals before the break as Fabregas side-footed home his second of the evening on 37 minutes before releasing Alexis with a fine pass over the top for the former-Udinese forward to grab his brace.
And it took the Spanish international just a minute after the break to seal his first hat-trick for the club as this time he latched onto Andres Iniesta's pass before turning and firing low past Aouate.
With the game well won, manager Tito Vilanova then withdrew Iniesta, Fabregas and Pique with an eye to Wednesday's Champions League tie with Paris Saint-Germain.
However, there was some more concerning injury news for Vilanova as Alexis hobbled off down the tunnel just two minutes from the end with what appeared to be a muscular injury.
Real Sociedad strengthen their position in fourth as they stretched their unbeaten run to 12 games with a 4-2 win over Malaga.
Goals from Carlos Vela, Alberto de la Bella and Antoine Griezmann saw the hosts race into a 3-0 lead within the first half hour and Inigo Martinez added a fourth after the break as the Basques moved four points clear of Malaga.
And at the bottom Deportivo La Coruna took another huge step towards survival as they beat Real Zaragoza 3-2 to move off the foot of the table.
Deportivo are now 18th and just one point off Zaragoza who have yet to win in the league this year.
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