The midfielder struck after just 14 minutes to hand the Rojiblancos a vital three points in the race to be crowned Spanish championsAtletico Madrid beat Villarreal on Saturday to stay top of La Liga.
A bright start saw the table-toppers take a deserved lead courtesy of Garcia's 14th-minute header, which proved decisive in a game of precious few chances.
Jeremy Perbet nearly found an equaliser midway through the second half with a curling effort, but could only find the roof of the net.
Atletico's preparations for the game were affected by the hamstring injury sustained by Diego Costa in the 1-1 Champions League quarter-final draw at Barcelona in midweek, and they struggled to find their usual incisiveness in the final third in the absence of their top scorer.
However, a combination of Garcia's ninth Liga goal of the season and typically dogged defensive resistance secured a vital three points for Diego Simeone's side.
The win continues Atletico's unbeaten league run at the Vicente Calderon, which now stands at 18 games, and leaves them four points ahead of Barca at the top of the table ahead of the reigning champions' clash with Real Betis later on Saturday.
Atleti playmaker Diego struck a thunderbolt at Camp Nou on Tuesday, and the Brazilian nearly produced another stunning strike within the opening two minutes here, meeting a Koke corner on the edge of the box before powering a volley over the bar.
Villarreal failed to heed that early warning and were behind 12 minutes later, when another Koke corner found Garcia, who rose unopposed to plant a header past former Atletico keeper Sergio Asenjo from seven yards.
Simeone's men struggled to build on their early advantage, though, with the hosts' attacking threat noticeably weakened without Costa, who has scored 33 goals in all competitions this term.
However, Atletico’s resilient defence - the best in La Liga, having conceded just 22 times in 32 outings - restricted Villarreal's creative freedom in the final third for much of first half.
Perbet did manage to get behind the hosts' defence after 32 minutes, but his flashed ball across the box eluded both Trigueros and Cani.
Atletico striker David Villa forced a smart save from Asenjo seven minutes after the break, as the hosts looked to muster a second goal and calm nerves among the home faithful.
Villarreal began to find more of a rhythm as the second half wore on, with Cani wasting a good opportunity just after the hour, harmlessly dragging wide after some good link-up play with Tomas Pina.
The visitors continued to press, and nearly restored parity 10 minutes later when Perbet curled a looping shot onto the roof of the net with Thibaut Courtois well beaten.
That was as close as Villarreal came, though, with Courtois remaining relatively untested for the rest of the game as Atletico took another huge step towards a first Liga title since 1996.