The Sweden striker scored a first-half penalty, after Alexandre Pato was fouled, and then set up Boateng's clincher in the closing stages.
With Juventus, level on points with Milan, winning at Lecce, and Udinese having done so against Cesena earlier in the day to temporarily nudge ahead, the victory was vital to keep the Rossoneri on top of the pile.
Alessandro Matri scored the only goal of the game for Juve to see off bottom side Lecce.
Matri headed home from close range after 27 minutes to settle a game in which neither side made the most of plenty of chances.
Udinese kept the pressure on the top two with a convincing 4-1 win over struggling Cesena at the Stadio Friuli.
Antonio Di Natale started and finished the scoring for the Bianconeri, with Citadin Eder giving the visitors hope with an equaliser in the 39th minute. Kwadwo Asamoah and Dusan Basta scored the home side's other goals in the second half as Cesena struggled with 10 men following the dismissal of Maurizio Lauro on the hour mark.
Francesco Totti struck twice from the penalty spot to end his goalscoring drought and fire Roma to a 2-0 victory over Chievo at the Stadio Olimpico while Napoli were 3-1 winners away to Palermo in the evening game.
Goran Pandev gave Walter Mazzarri's side the lead 10 minutes before half-time and Napoli extended their lead with second-half goals from Edinson Cavani (54) and Marek Hamsik (60). Fabrizio Miccoli (89) grabbed a late consolation for the Sicilians.
Cagliari moved above Genoa on goal difference after beating them 3-0 at the Stadio Sant Elia, in Pasquale Marino's first game as Genoa boss.
Joaquin Larrivey put Cagliari ahead from the penalty spot in the 12th minute and Victor Ibarbo doubled their lead early in the second half. An own goal from Andreas Granqvist in the 72nd minute compounded a miserable day for the visitors.
Stevan Jovetic bagged a brace as Fiorentina cruised to a comfortable 3-0 victory at Novara. The Montenegrin was on target in either half to take his tally for the season to nine while Riccardo Montolivo also weighed in with his first of the campaign as Novara meekly surrendered at Stadio Silvio Piola.
Bologna were 2-0 victors over Catania. Substitute Nicolo Cherubin put the hosts ahead early in the second half before Catania lost Marco Biagianti to a red card 12 minutes from time and Marco Di Vaio sealed victory at the death with Bologna's second of the match.
Diego Milito scored twice as Inter Milan walloped Parma 5-0 at the San Siro on Saturday night.
The Argentinian netted either side of a Thiago Motta effort in a one-sided first half as Inter got off to a flying start in 2012.
Giampaolo Pazzini and Marco Faraoni struck after the break to help Inter move to within five points of Serie A leaders and city rivals AC Milan.
They remain in fifth place, but closed the gap on Lazio to just one point after the Rome side went down 4-0 at Siena.
The visitors were 3-0 down at the break, conceding two penalties and having goalkeeper Albano Bizzarri sent off in a first half to forget.
Mattia Destro opened the scoring before Emanuele Calaio converted twice from the spot, with Bizzarri seeing red for bringing down Destro to give away the second penalty on the stoke of half-time.
Destro then got a second 10 minutes from time to complete a comprehensive win.