Playing at the home of the Boston Red Sox - and with principal owner John Henry watching on - Brendan Rodgers' side conceded a 90th minute effort to Marco Borriello.
It was a game in which clear-cut chances came at a premium for the teams, though despite the result, it proved another good work out for the Reds in their third fixture of the summer so far.
The pre-match team news confirmed starts for Sebastian Coates and Jose Enrique, while summer signing Rickie Lambert retained his place in the line-up after making his debut against Preston at the weekend.
There was a familiar foe in the opposing team in the form of former Arsenal and Chelsea defender Ashley Cole, who came in to make his Roma debut.
A moving tribute to the Liverpool fans who died at Hillsborough preceded kick off, with Fenway observing a minute's silence while 96 red balloons were released into the Boston sky.
Two years have passed since the teams last met at baseball's most iconic venue. On that occasion, Roma ran out 2-1 winners as Rodgers began life in the Liverpool hot seat.
Much has changed at Anfield in the 24 months that have since passed, with a sold-out stadium eager to see the side that exhilarated the Barclays Premier League last season up close.
However, with temperatures in the US city having easily exceeded 30 degrees all day, the humid conditions meant for a tepid start in front of the Green Monster.
And Liverpool were forced into an early reshuffle when Fabio Borini indicated to the bench he needed to come off after a heavy fall, meaning Emre Can entered the action as a 12th minute substitute.
A first effort of note at goal did not arrive until 20 minutes when Philippe Coutinho's free-kick from the left sizzled just beyond Lukasz Skorupski's far post.
It was all Liverpool in terms of possession in the opening exchanges; however, the Serie A side should have taken the lead when Cole scampered into space behind the Reds' rearguard down the left and lofted a ball into the danger zone. The toe of Francesco Totti was able to meet it, but could only stab wide of the upright.
Just before the break, a well-worked move at the other end resulted in a shooting chance for Lambert, but his effort cannoned against a defender before it could trouble Skorupski.
The England forward had another opportunity moments after the re-start - this time his hooked effort from Martin Kelly's cross was blocked by Alessio Romagnoli.
Lambert did get effort on target soon after, though Skorupski was equal to his near-post drive.
Just after the hour-mark, an energetic burst into the area from substitute Kris Peterson resulted in the youngster having an effort repelled. It broke for Coutinho on the edge of the box, but he could only drive into a body of Roma players.
With 13 minutes remaining, Jordan Henderson was introduced into the action for his first appearance since returning from World Cup duty with England.
Roma almost snatched a late winner when Antonio Sanabria strode into the area and pinged a low effort towards the bottom corner, but Brad Jones was able to thwart with a one-handed save.
However, from the resulting corner, Borriello was able to steer home via a deflection off Daniel Agger to secure a late win for Roma.