Inter had the best chances in the first half, as the crossbar replied Hakan Calhanoglu’s shot from inside the penalty area.
Liverpool struggled until coach Jurgen Klopp made several changes in the second half, so substitute Firmino scored with a header from a corner kick in the 75th minute.
With the collapse of Inter’s resistance, the team began to make mistakes and Salah pounced on the ball when the Italian team’s defense failed to remove it from inside the penalty area and fired a low shot into the net seven minutes before the end.
Even with the absence of the away goals rule, the victory gave the 2019 European champions an advantage before the return leg on the eighth of next month at Anfield.
Liverpool won all seven of their Champions League matches this season, extending their longest winning streak in the European Cup.
Inter, who reached the knockout stages for the first time in a decade, were the better party initially in front of their few fans as a result of the measures to combat the Corona virus.
Argentinian Lautaro Martinez hit the ball outside the goal before the crossbar countered Calhanoglu’s shot.
Liverpool tried a lot in the first half, but it lacked effectiveness and a header from Sadio Mane went over the crossbar.
Liverpool’s position did not change after the break, while the final touch failed Inter.
The host paid the price when Firmino silenced the crowd at San Siro, turning a corner kick from Andy Robertson with a header.
This is the Brazilian striker’s 11th goal as a substitute in all competitions this season, the best record for a substitute under Klopp’s leadership.
Salah added the second goal with a shot that changed direction when VanDyke set up Trent Alexander-Arnold’s pass for the Egyptian captain.
Salah scored the net in Liverpool’s last eight games away from home in the Champions League, the second longest streak for the player after Cristiano Ronaldo between 2013 and 2015.
Liverpool did not perform as usual, but did enough to get the job done.
This is the sixth time that Liverpool has won the first leg away in the Champions League and succeeded in qualifying in all previous times.