Bremen's coach Robin Dutt was under pressure to deliver the points after a run of poor results, and the delight on his face come the final whistle said it all as the northern Germany side returned to winning ways to pull away from the relegation zone.
Garcia was the match-winner with his 74th-minute strike, but Bremen were worthy winners against a Leverkusen side who remain seven points behind league leaders Bayern Munich, who have a game in hand.
The tension was palpable at the Weser Stadion as Bremen took to the field looking for their first win in six games.
Having shipped 20 goals in their last five games, it was no surprise that they started the game cautiously.
Leverkusen failed to take advantage, though, and apart from a couple of Stefan Kiessling headers, they rarely threatened Raphael Wolf in the Bremen goal.
Nils Petersen was Bremen's most dangerous outlet, but he sliced a left-foot shot just wide of the post early on in the first half before sending an angled effort sailing over the crossbar just shy of the hour mark.
Garcia was at the centre of everything for the hosts, who started to emerge from their shells in the second half and seek a winner.
They found it in extraordinary circumstances in the 74th minute.
Aaron Hunt sent the ball to the feet of Cedrick Makiadi, who went down inside the penalty area and was calling for a penalty.
The referee did not need to make that decision, though, as Garcia stole in to stroke the loose ball into the bottom left-hand corner, sparking wild celebrations both on and off the field.
Eljero Elia could have made it two minutes later, but he seemed too casual about his chance, which was saved.
There was plenty of nail-biting in the stands and Leverkusen's liveliest player Emre Can saw his shot blocked by a Bremen defender, although it seemed like the whole of the stadium had built the wall to keep his effort out.
The final whistle was met with cheers of relief and joy as Bremen finally picked up maximum points again to move up to 11th.