The Sweden striker smashed the ball into the roof of the net from close range in the 63rd minute for his 15th league goal of the campaign to end Mallorca's stubborn resistance and lift his side to 74 points from 29 matches.
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Barca have been relying on a flood of goals from league top scorer Lionel Messi to keep their title bid on track but coach Pep Guardiola started with both the Argentina forward and fit-again Spain midfielder Xavi on the bench.
Mallorca, who had won all but one of their 13 home matches, almost stunned the visitors in the second minute when Aritz Aduriz smashed a shot against the post and Gonzalo Castro forced a fine save from Victor Valdes with a follow-up shot.
After weathering the early storm, Barca began to exert their customary control and Mallorca goalkeeper Dudu Aouate reacted well to palm away a Gabriel Milito header in the 17th.
The Israeli goalkeeper twice denied Ibrahimovic and forward Jeffren, handed a rare start with France captain Thierry Henry not included in the squad, shaved the bar with a powerful strike just before the half hour.
Mallorca midfielder Borja Valero gave the visitors a scare when he curled a freekick against the post shortly before halftime, although Valdes, who is pushing for a place in Spain's World Cup squad, looked to have his goal covered.
LATE PRESSURE
The introduction of Messi and Xavi early in the second half gave Barca a fillip and it was from Xavi's corner that the ball eventually found its way to an unmarked Ibrahimovic who gave Aouate no chance.
The Sweden striker showed his versatility shortly after when he used his back to divert a deep Pedro cross into Messi's path but the Argentine's powerful shot flew over the bar.
Messi squandered another chance to double Barca's lead in the 83rd when he carved an opening at the edge of the area but skewed his left-foot strike well wide.
The Catalans survived some late pressure and the defeat leaves Mallorca in fourth on 47 points, two ahead of Sevilla, who play at Villarreal on Sunday in new coach Antonio Alvarez's first match in charge.
"I scored another goal but the important thing was the win," Ibrahimovic said in a television interview.
"It was a hard match and they were difficult opponents but in the end we got the three points."
In the late kick-off, third-placed Valencia had Nikola Zigic sent off for a second yellow card just before half time in a bruising clash at promoted Real Zaragoza.
Already 1-0 down after Carlos Diogo's thumping 41st-minute opener, Unai Emery's side crashed to a 3-0 defeat that leaves them 21 points behind Barca on 53.
Earlier, midfielder Alejandro Alfaro scored from the spot in the 86th minute to snatch a 1-1 draw for relegation-threatened Tenerife at Malaga.
