Garcia passed up a glorious opportunity to put the visitors ahead nine minutes into the second half when he completely missed his kick after being picked out unmarked by Boudebouz, and Cristian Tello clipped the outside of a post with 21 minutes remaining.
The 25-year-old - who moved to Madrid from Benfica in 2014 - has helped Atletico up to second in La Liga, while the Spanish outfit are preparing for their Europa League semi-final showdown with Arsenal.
Diego Simeone's side are favourites to win the competition and Sky Sports' Spanish football expert Gibson stressed the need for Arsenal to be controlled in possession to keep Atletico's risky attacking players quiet.
After Atletico's goalless draw with Real Betis on Sunday, Oblak was asked about his future at the club.
Las Palmas was relegated to Spain's second tier after losing 4-0 at home to Alaves.
Atletico, who go to Emirates Stadium on Thursday, have kept 11 consecutive clean sheets at home in all competitions.
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Aissa Mandi headed a Fernando Torres effort off the line and Saul Niguez struck the bar as Atletico also came close, but neither side could earn a victory.
Atletico head to London for their Europa League semi-final first leg against Arsenal on Thursday. We made important changes and the players responded, I had to rotate to ensure we had fresh players.
Equally frustrating will be the realisation their remote title hopes are nearly over, they have just four games more to play and trail Barcelona by 11 points.
"There is pressure, but the nice part of the season is coming now, the games for which we have worked hard, and we will try and give our best". "If I continue, we will grow together and if not, the club will grow as well".
It is an impressive feat masterminded by Abelardo Fernandez who took over in December with the Basque side bottom of the table.