The last strike, in 2008, lasted 57 days
The in-form forward broke the deadlock on the hour mark and Raul Garcia added a second moments later with Valencia’s resistance broken.
Costa then missed a penalty but converted a second with nine minutes to go, his 17th league goal of the season putting him level with Real’s Cristiano Ronaldo at the top of the scoring charts.
“You need to show personality and fight for your achievements so after missing the first penalty I wanted to take the second,” Costa told reporters. “Valencia played well in the first half and we knew that we had to do a bit more especially in attack which we did.”
Atletico are level on 43 points with Barcelona who beat Villarreal 2-1 on Saturday while third-placed Real Madrid lost further ground following a 2-2 draw at Osasuna.
Atletico started slowly with Gabi Fernandez and Tiago Cardoso quiet in the engine room and there were only flickers of life from their forwards. They upped their level after halftime and Costa dribbled in from the left wing with Victor Ruiz backing off before slotting home.
Minutes later they were further in front when Raul Garcia knocked in a loose ball in the area. Costa was then upended in the area by Ruiz and took the penalty himself but Diego Alves saved well with his feet.
Atletico were now ripping open the Valencia defence and Antonio Barragan fouled Costa in the area before the striker found the top corner with his spot-kick.
Earlier, Real Sociedad bounced back from their Champions League exit with a resounding 5-1 win over bottom side Real Betis and Sevilla and Athletic Bilbao shared the spoils in a 1-1 draw. Bilbao, fresh from beating leaders Barcelona last time out, were looking to consolidate fourth place but conceded an early goal from Alberto Moreno.
The last strike, in 2008, lasted 57 days
Monthly supply of 100,000 metric tonnes of crude oil will be secured until the end of 2025
China issues red alert, warns of gales and heavy rain
The pair tangled while battling for third place behind winner Oscar Piastri of McLaren and Ferrari's Charles Leclerc
Transaction includes approximately 86 million shares of Ma’aden and $150 million in cash
Celebrity endorsements rarely carry enormous weight, but the hugely popular Swift is seen as being in a class of her own
Zelenskiy is due to meet with US President Joe Biden this month and will present a plan for ending the war
Brazil has been parched by a historic drought that experts link to climate change and which has sparked what authorities have called a 'fire pandemic'