Garcia struck just before halftime on Sunday to give Atletico the victory that took them to a club record 88 points, six above second-placed Real Madrid who beat Osasuna on Saturday and still have a game in hand of their city rivals.
Barcelona, in mourning following the death of former coach Tito Vilanova on Friday, came back from 2-0 down to win 3-2 at Villarreal and move to 84 points with three games left.
Lionel Messi hit the winner in a dramatic finale.
“We were playing with fire. We were not playing that badly but the goal before halftime was a blow for us. We then went further behind but kept fighting until the end because this is what we have to do until the end of the season,” Barca midfielder Andres Iniesta told reporters.
“We still have a small hope in the league, it is not down to us but we need to battle to the end.”
Atletico were not at their best and lacked their usual high intensity, possibly a result of tiredness after a gruelling campaign and this week’s tense 0-0 draw in the Champions League semi-final, first leg against Chelsea.
However, they took another step towards the title despite having Juanfran red-carded in stoppage time following a wild challenge on Pablo Piatti.
“We need to continue to work hard and believe in ourselves,” goalscorer Garcia told reporters.
“It was a tough game and the word team is very important for us as we are all fighting for each other. At the moment it is all going well.
“More important than that I scored is that we won.”
The challenges are coming thick and fast for Atletico with this week’s Champion’s League return at Chelsea looming large.
“Now we are now focusing on Wednesday (against Chelsea) and we need to go out to win,” Garcia said.
“We are expecting a similar game to before with Chelsea making it very difficult.
Coach Diego Simeone chose not to rest any players ahead of their showdown with Chelsea but many looked a little jaded as Valencia took hold of midfield.
Valencia could have gone ahead in the opening minute when Daniel Parejo shot wide from the edge of the area.
Atletico came into the game and although Diego Costa saw little of the ball in attack David Villa, alongside him, curled a dangerous effort just wide of the post.
The visitors went ahead after 43 minutes with Garcia’s flicked header after keeper Vicente Guaita came off his line.
Costa wasted two good chances in the second half but at the other end Atletico were also lucky not to concede.
Jonas and Sofiane Feghouli both went close and in a tense finish Juanfran was dismissed for a rash challenge.
Atletico’s win made it imperative that an injury-plagued Barca followed suit and they did – just.
Cani and Manuel Trigueros gave Villarreal a two-goal lead with goals either side of halftime.
However, own goals by Gabriel, who deflected in a Dani Alves shot, and Mateo Musacchio, who headed into his own net, levelled the scores before Messi had the final say with a typically clinical finish seven minutes from time.
Athletic Bilbao boosted their hopes of a place in the Champions League place with a 3-1 win over rivals Sevilla and are now six points clear in fourth.
(Editing by Martyn Herman)