The 25-year-old more than compensated for Lionel Messi's absence with a scintillating display that saw him score a magnificent hat-trick and play a key role in Sanchez's double
The Catalan giants were irrepressible with both Cesc Fabregas and Alexis Sanchez putting in first-rate performances. The pair combined magnificently to end the first half with two goals and two assists each, before the former Arsenal man, operating as a false nine in the absence of Lionel Messi, completed his hat-trick soon after the restart.
Barca's superiority was clear from the off as they dominated possession with Andres Iniesta performing brilliantly in midfield, seemingly able to cut apart the Mallorca defence with a scything pass or a searing dribble.
It took 20 minutes for Tito Vilanova's men to break the Islanders' resistance and it was Fabregas who, sliding the ball past Dudu Aouate after a magnificent one-two with Sanchez, ended a run of nine Liga outings without a goal and opened the scoring.
Two minutes later the advantage was doubled by Sanchez as he followed up from Fabregas' initial effort with a simple finishing giving him his third Liga goal of the season.
The Blaugrana were relentless in attack and after Aouate had kept out Iniesta, Sanchez missed a golden opportunity to grab the third as he failed to divert the ball on goal from inside the six-yard box.
Alfaro then failed to halve the deficit with a header in the 35th minute and it proved to be extremely costly as another two goals for the hosts came in the following three minutes.
Fabregas bagged his second of the night after dropping deep and playing another give and go with Sanchez, bursting into the area to receive the pass and place it into the bottom corner.
The former Arsenal man then returned the favour, clipping a beautiful ball over the top to Sanchez who used the space between the centre-backs to double his tally for the night.
There was no let up after half time and with just 50 minutes of the second half played Fabregas became the first Spaniard to score a hat-trick for the club since Luis Enrique in 2001, latching onto Iniesta's pass and checking back inside of Kevin before rolling the ball into the bottom corner.
Mallorca thought they had pulled one back four minutes later when Alfaro stabbed the ball in at the back post, only to see the referee's assistant raise his flag for a dubious offside decision.
Cristian Tello and Gerard Pique both came close to finding the Blaugrana's sixth of the night, though any applause that would have been received may not have matched the rapturous reception for Eric Abidal as he marked his return following a liver transplant in the 70th minute.
In the end there turned out not to be another goal for Barcelona but the comfortable win restores their 13-point advantage at the top of La Liga following Real Madrid's win earlier on Saturday. Mallorca, meanwhile, fall to the foot of the table after Deportivo managed to pick up a win against Real Zaragoza.