Waelti opened the scoring for Arsenal in the 15th minute, snapping up a clearance from a corner and belting it into the net, and Maanum made it 2-0 seven minutes later with a powerful run and finish.
Liverpool had their fair share of chances from set pieces, with Irish defender Niamh Fahey going close with a header from a second-half corner and then following that up with a shot that flew just wide a minute later.
However, ultimately the Reds failed to score for the third league game in a row.
The win lifts Arsenal, who have yet to concede a league goal this season, back to the top of the table on 12 points after four games with previous leaders Manchester United beating Leicester City 1-0 later on Sunday.
Nikita Parris scored the only goal of the game in the 34th minute to secure all three points for United.
On Saturday Jamaican striker Khadija Shaw scored either side of the break to help Manchester City to a comfortable 3-0 win over Tottenham Hotspur, while Lucy Graham's goal just before the hour mark gave Everton a 1-0 win at Aston Villa.