Atletico play Barca at the Camp Nou on Saturday and were given fresh hope of a resurgence when struggling Villarreal, inspired by the brilliant Santi Cazorla, led the Catalans 4-2 going into the final minute.
But Messi, who had started on the bench, drove in a free-kick in the 90th and in the 93rd, Suarez fired in a devastating half-volley to earn Barca a 4-4 draw and an unlikely point.
Combined with Atletico's earlier 2-0 victory over Girona, the result means the gap at the top is reduced to eight points ahead of this weekend's top of the table meeting but Ernesto Valverde's side celebrated Suarez's goal like it was a winner.
"In the end it is only a point but there is a certain feeling after coming back from two goals down in the last minute," Valverde said.
Cazorla, meanwhile, sank to his knees, a chance spurned for Villarreal to pull four points clear of the relegation zone, with Celta Vigo, now only two behind, still to play Huesca on Wednesday.
They had come from two down, as Samuel Chukwueze and Karl Toko Ekambi cancelled out early goals from Philippe Coutinho and Malcom. Vicente Iborra and Carlos Bacca looked to have sealed an incredible win, only for Messi and Suarez to intervene.
The pair have now scored 51 goals between them in the league this season, just one shy of the total managed by Real Madrid.
"The spirit we showed at the end, to refuse to give in, to come back in the last minute - we showed that we want to win this league," said Suarez.
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