Cardiff started slowly but Hope Suominen, Amy Wathan and Kelly Aldridge all saw chances wasted as the first half progressed.
The second half was more of the same with Enfield defending well to keep out a determined Cardiff side but the hosts eventually broke the deadlock with a screamer fired in by Chloe Lloyd from 25 yards.
Elsewhere, goals from Charley Wilson, Jess Frampton and Gemma Simmonds gave Portsmouth – who also made the final-four stage last term – a hard-fought 3-2 win at Keynsham Town.
Southern Division pacesetters Coventry United fared worse though, and were knocked out by C & K Basildon after Karissa Rooney’s looping first-half goal secured a 1-0 win.
Newcastle United, leaders of the Northern Division after two games, were also knocked out after a 2-1 defeat at home to Bradford City.
The Bantams took the lead late in the first half after Katie Nutter’s right-footed shot deflected off the sliding Claire Pitt, leaving Laura Wareham stranded.
Newcastle should have equalised before the break but Lizzy Campbell lofted a good chance over the bar.
The second half saw the hosts begin to take control; that was until Charlotte Stuart put in a high challenge on Pitt, forcing her off injured with Newcastle having used all three subs.
The visitors took advantage, Sarah Danby netting to double the visitors’ lead on 67 minutes after Hannah Campbell had pulled the ball back from the byline.
Newcastle still had the majority of possession despite having lost a player and picked up a consolation goal on 81 minutes, Beth Gardener curling a 25-yard free-kick into the top right corner.
Meanwhile, Blackburn Rovers beat fellow Northern Division side Loughborough Foxes 6-0, Nottingham Forest were emphatic 8-0 victors away at Leafield Athletic and Huddersfield Town ran riot in their 10-1 victory against Blackpool Wren.
