Laura Harvey's side led at the break courtesy of Kim Little's penalty before doubling their advantage in the second period with another spot-kick from the Scotland international.
It was the perfect response to Thursday's disappointing FA Cup semi-final exit at the hands of Chelsea, which Arsenal lost 2-0 despite dominating.
The visitors started brightly and forced Nicky Davies into action inside a minute trough Little's fierce effort, before Jordan Nobbs went close soon after.
Ciara Grant ensured Liverpool would not break the deadlock with a fine challenge to deny Australia international Emily Gielnik, signed from Brisbane Roar on Friday.
Little fired over shortly afterwards before Harvey's side were awarded a penalty five minutes before the break when the Scot was felled by Samantha Chappell inside the box. The midfielder stepped up to open the scoring.
With half an hour remaining Arsenal - and Little - had two. This time the 21-year-old's shot was handled by Lynda Shepherd and, once more, she converted from 12 yards.
Niamh Fahey hit a post before Gielnik fired wide after neat build-up play. But Arsenal saw out their third win of the season to maintain a 100 per cent start to the campaign.