Atletico Madrid came from a goal down to register a 2-1 victory over Getafe in a LaLiga match staged at Coliseum Alfonso Pérez on Tuesday evening.
Madrid found themselves trailing just before halftime as Jan Oblak put the ball into his own net to hand Getafe the lead.
In the second half, Levante were reduced to ten men after Carles Aleñá was sent off for a foul on Matheus Cunha as he left his studs on Brazilian's right calf.
In the 78th minute, Suarez grabbed the leveller with his left foot after receiving a beautiful cross from Mario Hermoso. Suarez then won it late in the 90th minute, heading home Sime Vrsaljko's cross past David Soria.
The win temporarily sent Madrid at the top of the table with 14 points, one behind second-placed Real Madrid who take on RCD Mallorca on Wednesday evening.
Athletic Club 1-2 Rayo Vallecano
At San Mames, Rayo Vallecano registered their third win of the season after beating Athletic Club 2-1.
Álvaro García gave Vallecano an early lead after just five minutes of play but Ismailla Siss put the ball into his own to bring Athletic Club on level terms.
In the 96th minute, summer signing Radamel Falco headed home from very close range following Bebe's beautiful cross to win it for the visitors.
Levante 0-2 Celta Vigo
Celta Vigo registered their first-ever win in the LaLiga this season after beating Levante 2-0.
Iago Aspas gave Celta the lead in the second half and Levante could have grabbed the equalizer but Roger Martí saw his penalty saved by the goalkeeper in the 71st minute.
Brais Méndez then ensured Vigo pick their first victory after he made it 2-0, five minutes to stoppage time.
Levante remain winless after six opening matches, drawing four games while losing twice so far this season.
See LaLiga standings here.