Lautaro Martínez put Inter ahead in the second minute and the Italian visitors had several chances to add to their lead before Suárez leveled against the run of play in the 58th with a strike from outside the area.
It was then Lionel Messi’s turn to take over late, when he dribbled past two defenders while gliding down the right flank before finding Suárez. The Uruguay striker used an excellent first touch to take the ball past Diego Godín before slotting in the winner.
Antonio Conte’s side had kept Messi in check for most of the match. But Messi, who had not played more than 45 minutes in any game this season due to injuries, saved his best for the critical moment to deal Inter its first loss of the season in all competitions.
“It is a valuable win against a direct rival,” Suárez said. “Halftime exists so you can correct your mistakes. The team found its patience.”
Barcelona share Group F lead on four points alongside Borussia Dortmund, who beat Slavia Prague 2-0 with two goals by Achraf Hakimi. Inter and Prague were left with one point from two matches.
In the first half Inter looked like the efficient machine that Conte has forged in Serie A, where his side lead the league after winning all six of its matches.
Conte barked orders non-stop from the edge of his area as his players beat Barcelona’s pressure with excellently coordinated one-touch passing combinations starting from their own box.
Martínez was in Inter’s starting 11 as a replacement of the injured Romelu Lukaku, who was ruled out due to a leg muscle injury.
Pique’s ill-advised attempt to make a tackle in midfield led to a ricocheted ball falling to Martínez, who raced into area and fired inside the far post.
Having gifted Inter an early lead, Barcelona were lucky to not be down by a bigger margin at halftime.
Barcelona defender Nelson Semedo had to close quickly to block Nicolo Barella’s shot that promised to put Marc-Andre ter Stegen in serious trouble in the 33rd.
Martínez came close to a brace when his powerful header drew a one-handed save from Ter Stegen. The Argentine then had another shot stopped by a hustling Semedo.
Barcelona coach Ernesto Valverde gave more attacking punch to his team by removing Sergio Busquets and sending on Arturo Vidal.
And Suárez revived Barcelona with his equalizer.
The striker collected a lofted ball from Vidal and smashed the ball from just outside the box into the far corner.
Barcelona immediately showed more fight, and their passes became crisper and cleaner. But Griezmann wasted a ball from Messi by shooting into the side of the net. And substitute Ousmane Dembele drove the ball over the crossbar shortly after replacing Griezmann.
Messi is still waiting for his first goal of the season. But his run before assisting Suárez showed that he can still turn a match around even while not in peak form.
With a burst of quickness, he juked past Kwadwo Asamoah on the right touchline and then cut back around another defender before linking up with his strike partner.
Messi started the match after being cleared to play by team doctors a day earlier. He had missed one match with muscle problem in his inner left thigh. Prior to Wednesday night, Messi had missed five matches due to injuries this season and been limited to just 120 total minutes in four appearances. (AFP)