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."
Earlier, Real Madridhad continued their own good run of late with a 5-1 demolition of Levante.
The visitors had taken a shock lead through Michel just after the half-hour mark, but their lead only lasted five minutes as Gonzalo Higuain scored a goal of the season contender with a wonderful volley from Xabi Alonso's cross.
Kaka then put the hosts ahead before the break from the penalty spot and Cristiano Ronaldo made the game safe with his 29th league goal of the season six minutes from time.
Substitute Mesut Ozil twice scored from close range in the dying moments to complete the rout.
Meanwhile, Bayern Munich set the record for the earliest Bundesliga title win on Saturday when they were confirmed as German champions for the 23rd time with a 1-0 win at Eintracht Frankfurt. Bastian Schweinsteiger scored the decisive goal to give Bayern their 24th win from 28 league games this season and seal their first major silverware since May 2010.
"We're a strong team with a great coach, it's fantastic to have won the title," said goalscorer Schweinsteiger.
It was the perfect preparations for Bayern as they look to defend their 2-0 lead from the first leg of their Uefa Champions League quarter-final tie against Juventus when the two sides meet in the second leg on Wednesday in Turin.
Juventus, meanwhile, stretched their advantage at the top of Serie A as a brace from Mirko Vucinic helped them to a 2-1 victory over a heroic Pescara and a 12-point lead over Napoli.
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