Russo made it seven goals in her past four games, in all competitions, with her double against Liverpool.
For the first time in four league games, Renee Slegers’ side made a bright start and went ahead as Baum had a shot deflected on to the crossbar before Russo opened the scoring.
A third league win of the season comes at a good time for Arsenal with three crucial matches coming up against Barcelona, London City Lionesses and Lyon.
They were pushed hard by Liverpool, who were unable to find a second equaliser despite efforts from Cornelia Kapocs and Mao Itamura.
The Gunners have now won 22 WSL games against Liverpool (D2 L4), the most victories any team has over a single opponent in the competition.
The Reds, who are now winless in their past five league games, travel to Brighton next weekend.