Both Borussia Dortmund, who beat Slavia Prague 2-0 on Wednesday, and Barca are on four points after two matches, while Inter and the Czech club have a point each, reports Efe news.
With the brace against Inter, Suarez has already doubled his goal total in the 2018-2019 Champions League, and the Uruguayan's return to form in European play couldn't have come at a better time for Barcelona, currently fourth in La Liga after seven matches.
The visitors, superior in all aspects of the game for the lion's share of the first half, took the lead in the 2nd minute with a goal by Lautaro Martinez, who took a deep pass and got past defender Clement Lenglet before beating keeper Marc-Andre ter Stegen with a low drive.
It was Inter's first goal at Camp Nou in nearly half-a-century.
Barca's first shot a header by Antoine Griezmann came only in the 15th minute as the reigning Spanish champions struggled to penetrate the Inter defence, while the Italian side remained a constant threat on the counter.
The hosts' best moments of the opening period came in the 20th minute, culminating in a shot by Sergio Busquets. Lionel Messi's free kick five minutes later posed no problems for Inter keeper Samir Handanovic.
Antonio Candreva doubled Inter's lead in the 27th minute, but the goal was disallowed for an offside.
Barca defender Nelson Semedo used his body to deflect Nicolo Barella's strike away for a corner in the 33rd minute. In the 37th, Ter Stegen made the stop of the night to deny Lautaro three minutes before dealing with a strike by Stefano Sensi.
While Inter started the second half with the same intensity, they found themselves facing an improved Barcelona side, especially with the entry of Arturo Vidal for Busquets in the 52nd minute.
After turning his first touch into a scoring chance, the Chilean international assisted on Suarez's equalizer in the 58th minute.
Griezmann hit the side of the net in the 61st minute, five minutes before he was subbed out for Dembele.
The contest was still deadlocked with six minutes left in regulation when Messi worked his magic to set up Suarez's game-winner.
( With inputs from IANS )