Everton began brightly with Anna Anvegard finding the back of the net in the fourth minute, and despite Town’s best efforts, the visitors scored again before the break with Valerie Gauvin grabbing her first before half- time.
Just five minutes into the second half Gauvin scored her second of the game. It ended up being too much for the Terriers who, despite their chances and efforts, failed to dent the professional outfit.
They conceded again just before the full-time whistle with Claire Emslie scoring a wonderfully hit volley.
Town manager Glen Preston said: “The performance is what we cared about, I thought the players from one to 17, were outstanding today.
“They stuck to the game plan as best as they could, the early goal was a bit of a setback, which I think could have really knocked their confidence, but the players responded brilliantly.
“At 2-0 at half-time we were still in the game, we created chances, not many but three or four pretty reasonable chances were created throughout the game.
“Someone said to me that that scoreline is the best a tier-three side has had against a tier-one side, so if that’s the case, then you can’t ask for anymore than that.”
Despite the result, Town will be proud to have broked their attendance record. A crowd of 1,115 was present the last time they played at the John Smith’s Stadium, a number broken a by a few dozen on Sunday.
Preston said: “It doesn’t matter if we have gained an extra 50, or 100, they are extra fans coming in, seeing what the women’s team is all about, what we are capable of, and today we will have shown what we are all about in terms of grit, tenacity, that Terrier spirit. Hopefully there is a few more people that will come down and support us on a regular basis.”
Sheffield United’s FA Cup challenge is also over as they were beaten 4-1 by Women’s Super League side West Ham United at Sheffield FC.
Neil Redfearn’s Blades were level at 1-1 after six minutes when Bex Rayner slid in to cancel out Melisa Filis’s opener, but West Ham assumed control with a double from Claudia Walker and a fourth from Dagny Brynjarsdóttir in the 63rd minute.
Elsewhere in the women’s FA Cup there were wins for Arsenal, Birmingham City, Reading, Durham, Chalrton Athletic, Southampton, Manchester United, Liverpool, Ipswich Town, Leicester City, Coventry United, holders Chelsea, Manchester City and West Bromwich Albion.