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 win 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 worth a victory.
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.
Rested along with Gerard Pique and Ivan Rakitic, it seemed Barcelona would be able to leave Messi on the bench as Coutinho tapped in a pass by Malcom, who then headed in Arturo Vidal's cross for a 2-0 lead after 16 minutes.
But Villarreal sprung into life, revived by Chukwueze, who pulled one back seven minutes later. A sumptuous flick by Iborra launched the counter-attack and Cazorla sent the striker clear. Chukwueze's shot struck the post but cannoned back to him and this time, he guided it into the far corner.
Any control Barcelona had increasingly gave way to chaos, particularly on the break, where Villarreal broke through almost at will. Toko Ekambi's equaliser shortly after half-time looked like a fluke but perhaps he meant it.
- Messi introduced -
He tore down the right wing and cut inside, with Marc-Andre ter Stegen stepping out to block what he expected to be a cutback. Instead, Toko Ekambi stabbed the ball inside the goalkeeper and into the far corner.
Messi warmed up and then came on in the 61st minute but it was Villarreal that pulled away. A minute later, Iborra nipped onto Manu Morlanes' pass and prodded it home before Bacca made it four with 10 minutes left.
Cazorla was again the instigator, his curled pass creating the chance, as Bacca skipped round Ter Stegen and slid in for what seemed like the win.
Instead, Alvaro Gonzalez was sent off for a second yellow card in the 86th minute and Messi lashed a free-kick in off the post to give Barca hope.
When Suarez drove in his thundering half-volley from the edge of the box, there were four seconds of the three added minutes remaining. Atletico Madrid were putting the finishing touches to their victory over Girona at the Wanda Metropolitano when Barcelona kicked off but they had to wait until the 76th minute for Diego Godin's opener.
They had VAR to thank too as the Argentinian's header was only allowed to stand after Antoine Griezmann had initially been ruled offside. Griezmann's lob added a second in injury-time.