Inter had the lion's share of serious chances but a number of saves from Samir Ujkani kept out an otherwise blunt attack.
Andrea Ranocchia's 74th-minute early cross, however, would be inadvertantly poked beyond Ujkani by Garcia to hand the hosts all three points.
Napoli had a thumping 5-1 win over bottom club Pescara as two goals each by Gokhan Inler and Edinson Cavani, one from the penalty spot, helped Walter Mazzarri's Napoli side stay two points behind Juve, who defeated local rivals Torino 3-0 on Saturday.
Inter are four points behind Juve on 31 after ending a run of three games without a win.
Stefan Savic scored both Fiorentina goals in a 2-2 draw with Sampdoria, the second a superb header, which earned a point after Nenad Krsticic and a Gonzalo Rodriguez own goal had seen Sampdoria equalise then take the lead. Savic's goals were his first in Serie A.
Fiorentina are in fourth place, equal on 29 points with Lazio and two behind Inter Milan, while Samp move up to 12th on 17 points.
"Honestly I'm happy with our position, it's a shame that it's not the end of the season now, or at least within a couple of games," Fiorentina coach Vincenzo Montella said.
"We came up against a Sampdoria side that caused us problems, and while we weren't brilliant we had enough opportunities to win."
Lazio are six points off the pace in fourth spot after beating Parma 2-1 thanks to a 25th-minute effort from defender Giuseppe Biava and Miroslav Klose's ninth league goal of the season.
Ishak Belfodil pulled one back for Parma in the 66th minute, converting the rebound after his penalty was saved.
AS Roma are sixth after coming back from a goal down to win 3-1 at lowly Siena.
Two goals from rejuvenated former Siena striker Mattia Destro and one by Simone Perrotta gave Zdenek Zeman's side a deserved victory in a match where they missed a hatful of chances.
A first half hat-trick from Alberto Paloschi and a last minute tap-in by Adrian Stoian gave Chievo a 4-2 victory at fellow strugglers Genoa and their first away points of the season.
Genoa's fourth straight home defeat saw them slip into the bottom three with 12 points, only one ahead of Pescara.
Bologna beat Atalanta 2-1 thanks to a deflected free kick from Alessandro Diamanti in the 16th minute and a second-half goal from former Atalanta player Manolo Gabbiadini while Udinese stayed in mid-table despite a 4-1 rout of Cagliari