Espanyol skipper Garcia scored one goal and set up another for his team as they claimed a rare victory away from home.
The Barcelona-based club had won just once in their past 10 matches on the road in all competitions but that record was not enough to see Malaga notch a much-needed victory.
Espanyol hit the front in the 33rd minute when Christian Stuani found space with a smart turn and, as Malaga's defenders flocked to him, the Uruguayan released Garcia down the right and the veteran striker lashed the ball into the net.
Malaga responded immediately, although the goal should have been ruled out for offside.
Roque Santa Cruz found Pablo Perez at the top of the penalty area and, while the midfielder was slightly goal-side of Espanyol's last defender Juan Fuentes, the flag stayed down and Malaga's midfielder made no mistake with his shot across Kiko Casilla.
But Espanyol's feelings of injustice would have been assuaged with 14 minutes remaining at the Estadio La Rosaleda when Garcia produced a brilliant defence-splitting pass to pick out Pizzi on the right and the Portuguese forward slammed the ball inside the far post from a tight angle.
Perez was sent off two minutes later to make matters worse for Malaga.
The win took Espanyol to eighth in the La Liga table with 40 points - ahead of games on Wednesday and Thursday - and Malaga remain 13th with 32.
Depending on results, Malaga could fall as low as 17th by the end of the 30th round - just one spot above the relegation zone.
Malaga avoided dropping one position on Tuesday as Elche, who sit 14th, were held to a 0-0 draw at home against fourth-placed Athletic Bilbao.
The result took Elche to 31 points for the season after they edged possession against the Basques but failed to convert one of their 12 shots for the game, with just two on target.
Bilbao were equally wayward in the forward third with one shot on target from eight attempts, as they stayed fourth in the UEFA Champions League play-off spot, moving up to 56 points; 13 behind third-placed Barcelona and nine ahead of Sevilla, who sit fifth.
