Suarez scores 2 as Barca rallies late to beat Rayo 3-2
Suarez then scored his second goal to complete the fightback when he was left unmarked to stab in Sergi Roberto's cross at the far post.
"The game was very difficult for us, but we knew how to turn it around," Suarez said. "You can lose leagues at grounds like this one."
Barcelona increased its league lead to four points over Atletico Madrid, which drew at Leganes 1-1, and Alaves. Alaves visits Eibar on Sunday.
But the hosts swung the match in their favor when Jose Pozo scored from outside the area with a shot that went in off the bottom of the upright in the 31st.
After Suarez hit the post, substitute Alvaro Garcia put Rayo ahead in the 57th when he finished off a header by Raul de Tomas that came off the woodwork.
Suarez moved to the top of the league scorer list with nine in 11 rounds.
The Uruguay striker has six goals since Messi broke his right forearm on Oct. 20 against Sevilla, including a hat trick last weekend against Real Madrid. He also set up a goal in a 2-0 win over Inter Milan in the Champions League with Messi out.
Valverde said they will see if Messi is fit to travel for Tuesday's Champions League match at Inter Milan.