Bristol Academy forced a corner just 2 minutes in but the header was a yard or two wide of the far post and it proved to be a rare first half threat from the Vixens.
Julie Fleeting hooked an effort over the bar when a throw-in was headed on and Jordan Nobbs volleyed over from 20 yards out.
Siobhan Chamberlain had to punch clear twice in quick succession, from Steph Houghton's drive and Nobbs' free-kick.
Player of the match, Kim Little opened the scoring on 19 minutes, turning a defender on the edge of the box and firing low past Siobhan Chamberlain.
Julie Fleeting doubled the lead after 33 minutes, having been denied by the crossbar seconds earlier. Chamberlain pulled off a good save but at the cost of a corner aand from a Niamh Fahey cross Fleeting headed home powerfully.
Fleeting also saw a header land on the roof of the net and at the other end, Emma Byrne had to rush out to collect at Fishlock's feet.
Fishlock was injured under an aerial challenge from Katie Chapman just before the break but Helen Bleazard's 30-yard free-kick was well over.
Early in the second half, Daley delivered a free-kick into the box but just out of the reach of a forward's boot as Byrne collected.
Kim Little forced a smart low save from Chamberlain, following Yankey's pull-back.
Grace McCatty went on a good run for Bristol midway through the second half, which eventually led to a free-kick 22 yards out and Daley's strike hit the bar and went over.
Bristol did have a better second period but Little looked likely to get her second from Houghton's long free-kick until Chamberlain made a fantastic block with her foot. Little again went close but Gemma Rose got a vital block in for a corner.
Danielle Carter had a chance seconds after replacing Yankey, charging down a clearance from the keeper, the angle was too tight for her header.
Arsenal: Byrne, Houghton, Flaherty, Grant, Nobbs, White, Fleeting (Beattie, 80), Yankey (Carter, 90), Little, Chapman (c), Fahey.
Unused Subs - Spencer, Tracy, Coombs.
Bristol Academy: Chamberlain, Yorston (c), McCatty, Bleazard, Daley, Heatherson (Green, 84), Fishlock (Billson, 45), Dykes, Hoogendijk, Culvin (Clark, 68), Rose.
Unused Subs - Windell, Jones.
Pictured - Kim Little celebrates her goal. (TheFA.com)
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