On an at times nervy night at Meadow Park, Caitlin Foord’s first-half opener was followed by goals in the final ten minutes from Lotte Wubben-Moy and Vivianne Miedema as Jonas Eivedall’s side eventually sealed a reasonably comfortable on victory.
Having been well beaten in their opening group game against Barcelona, Arsenal have won three on the bounce and are six points clear of Hoffenheim with two games to play.
Eivedall’s side have a far superior goal difference and could secure their place when the Catalan club visit the Emirates Stadium next month.
Arsenal dominated possession for most of the 90 minutes against the Danish champions, but struggled to put the game out of sight.
Foord had finished well from Beth Mead’s cross to put the hosts ahead but Arsenal were frustrated for much of the second half after Mead had a goal ruled out for offside just before the interval.
An at times frantic Arsenal struggled to force or take openings and were grateful to their England forward again turning provider, Mead whipping in a delicious cross which was emphatically headed home by a charging Wubben-Moy.
And there was time enough left for Miedema to get on the scoresheet, the Dutch striker finishing typically cooly with a deft lift over the goalkeeper having been freed by a raking left-footed pass from Steph Catley.
Barcelona continued their perfect start to the defence of their WCL crown with a 5-0 drubbing of Hoffenheim.
Alexia Putellas’ calmly-taken first half penalty was followed by four second half goals as Barcelona confirmed their place in the knockout phase.
Arsenal face Manchester United, fifth in the WSL, in Leigh.