The deadlock was to be broken just seven minutes after the restart, however.
Malard darted infield from her left-wing position and spread play out to the far right for Jess Park.
Park identified Naalsund in a pocket of space at the centre of the area and the latter clinically dispatched a strike high into the goal.
Liverpool responded quickly and levelled the score from a scramble in front of the United goal shy of the hour.
A corner kick from the left led to pinball that was settled when Cornelia Kapocs nodded to Bergstrom and she tucked home.
Parity was frustratingly short, though. United instantly restored their advantage from a high press, Naalsund giving Falk no chance with her second strike.
The Reds kept searching for a second equaliser of the afternoon, but it was the hosts who were coming closest to changing the scoreline again.
A swerving Anna Sandberg corner from the right almost went all the way in as Falk tipped it off the crossbar.
The Liverpool ‘keeper also had to push away a Park half-volley in the closing stages.
United ultimately confirmed the points would be theirs in the 87th minute, Rolfo rasping in a finish from Hanna Lundkvist’s near-post cross.
Team
Liverpool: Falk, Shimizu (Woodham, 82), Clark, Fisk, Bernabe (Enderby, 81), Nagano, O’Sullivan, Kapocs (Olsson, 86), Bergstrom (Csillag, 66), Thomas, Holland.
Unused subs: Kirby, Parry, Evans, Maclean, Bonner.
Next up
The Reds are back in WSL action on home soil next Sunday (February 8), with Aston Villa the visitors to St Helens Stadium.
Kick-off is 12pm GMT. Tickets and free coach travel can be booked here.
