Kim Little and Jordan Nobbs netted during an opening 45 minutes in which the Marta Tejedor’s side had to withstand a lot of pressure.
Blues somewhat turned the tables after the interval but openings came and went without finding a way through.
Tejedor made two changes from the pre-Christmas defeat to Manchester United in the FA Women’s Continental League Cup group stage.
Hannah Hampton returned in goal with Lily Simkin brought back in at full-back. Alex Brooks and Connie Scofield made way and were joined by Sarah Mayling, back from injury, on the bench.
Blues started brightly enough but found it tough to keep the ball and Arsenal led inside nine minutes.
Chloe Arthur’s header up in the air cushioned back across goal by Vivianne Miedema for the unmarked Little to convert at the far post.
Miedema had a far-post shot charged down by the alert Adrienne Jordan minutes later and the free-scoring Dutch striker was busy again midway through the first half, lofting over Simkin before cushioning a lob narrowly over the bar from no more than eight yards.
It was 2-0 after 23 minutes when Leah Williamson dinked over the Blues backline to find Nobbs in space and her quick, instinctive lob across goal on the run sailed over Hampton.
Blues almost replied immediately with Claudia Walker picked out on the right of the box but her firm rising drive across goal was pushed up and over by Pauline Peyraud-Magnin.
The match began to open up with Harriet Scott cutting out a low cross meant for Miedema with Lisa Evans arriving late to curl over from 10 yards with the goal gaping.
Lucy Staniforth hit the top of the bar from the corner flag for Blues via a touch from Peyraud-Magnin and then Jordan picked up a high ball at the far post, touching around Leonie Maier before scuffing her shot under pressure.
The deficit could have grown before half-time, Nobbs picking up on a loose ball on the edge of the Blues box and guiding into Miedema to wrap her foot around a shot on the swivel that pelted the angle of post and bar.
An Evans cross from the right then smacked the outside of the post with Hampton well placed to judge it but the ball came back out with Miedema who passed to the free Danielle van de Donk to clear the bar on the move from 10 yards.
Arsenal momentum was stifled after half-time and Blues gradually worked openings of their own.
Hampton closed down the angle brilliantly to save one-on-one from Miedema and grasped a point-blank header from Little following a slick passage of play.
Neither Abbi Grant nor Rachel Williams could seize upon a sloppy back pass that sold short Peyraud-Magnin as the tide steadily turned but the hosts still posed a threat on the break.
Miedema palmed off Scott who went down holding her face prior to a rasping drive that Hampton repelled before clutching a point-blank Jill Roord header at the death.
Arsenal: Peyraud-Magnin, Maier, Williamson, Schnaderbeck, McCabe, Walti, Little, Nobbs, van de Donk (Roord, 87), Miedema, Evans.
Unused subs: Quinn, Mead, Filis, Grant, Zinsberger (g/k).
Goals: Little 9, Nobbs 22.
Blues: Hampton, Jordan, Holloway, Scott, Simkin, Arthur, Staniforth, Whipp (Scofield, 64), Grant (Mayling, 64), Williams (Brown, 87), Walker.
Unused subs: Gregory, Brooks (g/k)
Referee: Elizabeth Simms.