Amid their successful Australian branding exercise there was a game to play, but Liverpool's Melbourne love-in hardly curled the toes as the Premier League side rambled to a 2-0 win over an undermanned but game Melbourne Victory at a sold-out MCG on Wednesday.

Until injury time Liverpool led by a solitary goal, scored by Steven Gerrard in the 32nd minute. The second – a tap-in by summer signing Iago Aspas – did not arrive until the final seconds and much to the delight of the majority of the 95,446 spectators it was Luis Suárez who served it up on a platter.

A day after Arsenal put in a second bid – £40m plus £1 – for his services, Suárez, playing his first match for Liverpool since biting Chelsea's Branislav Ivanovic's arm in April, played an 18-minute cameo, and in that brief period he linked well with Aspas. But the game appeared set to end 1-0 before the Uruguayan slipped his man on the byline then threaded a ball to the feet of the Spaniard. It was the highlight of a rather pedestrian second half.

In the 66th minute, sections of the crowd had begun chanting: "We want Suárez," and in the 72nd minute the Liverpool manager, Brendan Rodgers, obliged, sending the Uruguayan forward on, along with nine other substitutes.

With some of Victory's best players either injured or, such as Archie Thompson and Mark Milligan, on duty with the Socceroos at the East Asian Cup, there was a feeling before the match that Victory – still 11 weeks away from the start of the A-League season – would be exposed by the Premier League side.

But, amid an overwhelming sea of red in the stands, it hardly played out that way once the game began, and to their credit, Victory's back four played high up the pitch, and the Melbourne side, through the midfielder Billy Celeski, often found space down the centre of Liverpool's midfield.

For the first 20 minutes both sides had been content to pass and probe without any real menace, with the only decent chance falling to the busy and threatening Raheem Sterling in the sixth minute, following a long ball from Gerrard. But, pressured by Jason Geria, Sterling's first-time shot looped wide of the right hand post.

Liverpool then had a scare in the 10th minute when the Victory winger Connor Pain forced his way to the byline before cutting back dangerously, only for Liverpool to clear. Ten minutes later the Victory forward Andrew Nabbout drifted inside Andre Wisdom and forced a diving save from Brad Jones.

Content to sit back until this point, Gerrard fired a warning shot from outside the penalty area moments later, which Nathan Coe pushed wide. That was to prove a warning sign, as Liverpool opened the scoring with Gerrard's goal shortly afterwards.

A clever dummy from the Liverpool captain in the centre of the pitch allowed the ball to run to Joe Allen, who dribbled to the edge of the area before squaring for an unmarked Gerrard to shoot low to the keeper's left.

Liverpool dominated possession for the remainder of the half, Gerrard going close again after Jordon Ibe, scooting down the right flank, turned Leigh Broxham inside out and his cross was parried by Coe, but the skipper's hurried volley sailed wide.

Though his team struggled at times, Rodgers was happy with Liverpool's win, saying they were tactically sound and showed "lots of moments of quality".

Rodgers also praised Melbourne Victory and their coach, Ange Postecoglou, saying they had a similar footballing ethos. "They can be very proud of what they put on tonight. [The singing of] You'll Never Walk Alone at the beginning was a real tear-jerker. There's not many clubs in the world can do what we've done in the last week or so. Over 80,000 in Jakarta, over 90,000 here.

"It's a day that hopefully many of the supporters over here in Australia will never forget."

Liverpool will now travel to Bangkok for the final match of their international tour. Only time will tell whether that will prove Suárez's last outing for Liverpool.

Melbourne Victory (4-4-2): Coe; Geria, Leijer, Ansell, Galloway, Celeski, Broxham, Nabbout (Stella, 82), J Jeggo, Makarounas (Cristaldo, 86), Pain. Subs not used Thomas, Brown, Cristaldo, L Jeggo, Buceto, Murnane, Radonich

Liverpool (4-2-3-1): Jones (Mignolet, 72); Luis Enrique (Flanagan, 72), Wisdom (Agger, 72), Skrtel (Coates, 72), Johnson (Kelly, 72), Gerrard (Lucas, 63), Allen (Spearing, 72), Sterling (Alberto, 72), Henderson (Aspas, 72), Ibe (Downing, 72), Borini (Suárez, 72). Subs not used Assaidi, Robinson.

Attendance 95,446