Garcia's side left it late at the Stadio Olimpico - Alessandro Florenzi striking a 90th-minute winner after Ciro Immobile had cancelled out Mattia Destro's opener.
With Napoli beaten by Fiorentina on Sunday, the gap between Rafael Benitez's side and Roma stands at nine points going into their final nine games of the campaign.
Garcia considered the victory as a major boost for their hopes of securing the final automatic UEFA Champions League spot but refused to take anything for granted.
"This win is massive for us psychologically, that's why I was so happy," he said.
"Torino aren't a direct rival of ours so I decided to throw on the extra attacking players, even though it might have meant we lost. We needed to take a risk to win it.
"We were very lucky to score through Florenzi after he came off the bench: it just shows that you don't win with 11 players but with the whole roster.
"Second place? We'll have to wait a bit before we're there mathematically. What we can say is that we have a nine-point lead over Napoli tonight: it's a big lead."
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