Fern Whelan added to White’s first-half brace to complete the win for the Lady Pies, despite a late Nadia Lawrence consolation goal.
First round results
Doncaster Rovers Belles 2-1 Sunderland
Oxford United 0-2 Birmingham City
Yeovil Town 1-3 Notts County
Sheffield FC 2-0 Bristol City
Reading 1-3 Arsenal
Everton 0-1 Liverpool
Aston Villa 0-8 Man City
London Bees 2-2 Chelsea
(London Bees win on pens)
“We are all really pleased to be in the hat for the next round, that was our main priority,” said White.
“We are always looking to improve, and to get better, and our recent signings will only help us do that.
“They give us some fantastic midfield options and it adds another element to the team, and hopefully we can now push on and improve in the league and cups.”
Elsewhere London Bees stunned reigning FA WSL champions Chelsea on Saturday with a dramatic penalty shootout victory, with Merrick Will scoring the decider after finishing extra time with the score all square at 2-2.
An own goal from Gilly Flaherty and Jo Wilson’s strike put the Bees ahead after Beth England’s 25-yard opener for Chelsea, but the visitors – down to 10 players after Niamh Fahey’s sending off – sent the game to extra time thanks to Millie Bright’s stoppage-time equaliser.
“It was brilliant,” said Will. “We were hanging on and we might've got the win before the full-time whistle went but I'm happy I got on and helped the team towards victory.
“We came into it with not much pressure and I knew we could do it. We definitely went in there underestimated and I think that showed in our performance.”
Nikita Parris scored her first ever hat-trick for Manchester City in their 8-0 win away to Aston Villa, with Jane Ross and Jill Scott also among the goalscorers in the Midlands.
And after the disappointment of last week’s league draw with Liverpool, Parris paid tribute to her teammates’ determination.
“That’s my first hat-trick for Manchester City and I’m very proud of it, but it was all about the team performance,” she said.
“We’ve come off a disappointing performance in our league draw against Liverpool last week and we were determined to bounce back to winning ways.”
Meanwhile, Liverpool secured bragging rights in the Merseyside derby as they beat Everton 1-0, while Fara Williams bagged a brace as Arsenal triumphed over Reading 3-1.
Sheffield FC and Birmingham City scored two apiece in their victories over Bristol City and Oxford United respectively, and Emma Coates got her first victory as Doncaster Belles manager as they beat Sunderland 2-1.