The 32-year-old striker, who spent the second half of last season on loan at West Ham, steered the ball home from a 90th-minute corner through the legs of Jack Robinson, despite the close attentions of Daniel Agger.
Sunderland transfer target Fabio Borini was named in the Reds' starting line-up alongside Rickie Lambert, but the Italian was forced off with a shoulder injury in the 12th minute.
However, speaking after the match, Reds boss Brendan Rodgers played down the severity of the knock.
"He's only bruised it," said Rodgers. "He won't train now for the remainder of the trip here, but it's only going to be a few days before he's back training and playing again."
In front of a sold-out crowd, Philippe Coutinho was the stand-out player on show for Liverpool, against a Roma team that included former England left-back Ashley Cole.
After Coutinho had sent a 20th-minute free-kick just wide, Francesco Totti stabbed a good chance wide for the Giallorossi after being set up by Cole.
Lambert had several chances, and forced a fine save out of goalkeeper Lukasz Skorupski after the break.
Coutinho had another shot blocked from the edge of the area and Brad Jones made a one-handed stop to deny Antonio Sanabria before Borriello settled the affair late on.
Meanwhile, Liverpool owner John W Henry spoke about life after Luis Suarez for the Reds following the sale of the Uruguay striker to Barcelona.
"It was time for Luis and time for the club to make a break," said Henry. "He brought so much to the club but we brought a lot to Luis.
"I think you will still see a very explosive Liverpool offense."
Liverpool's next friendly assignment is against Olympiakos in Chicago on Sunday, a game in which Adam Lallana and Lazar Markovic are expected to make their Reds debuts.