Four days after booking their spot in the League Cup final, Sonia Bompastor's Women's Super League leaders ultimately eased through to the last eight on Sunday.
It was Everton who took the lead, with Sara Holmgaard finding the net in the 17th minute.
By half-time, Chelsea were ahead, though, thanks to a penalty from Catarina Macario and a stoppage-time goal from Mayra Ramirez.
Maika Hamano extended the advantage in the 71st minute before another penalty in stoppage time, this time converted by Sandy Baltimore.
Liverpool left it late to end the challenge of third-tier Rugby Borough, battling to a 2-0 victory.
Marie Hobinger finally broke the deadlock with six minutes remaining and Mia Enderby added a second two minutes into stoppage time.
It was a similar scenario for WSL basement side Crystal Palace against Newcastle, with Ashleigh Weerden and Abbie Larkin both scoring in the final 10 minutes of their 2-0 win.
London City are flying high in WSL 2 but they could not cause a huge upset against Arsenal. The Gunners, with Matildas stars Kyra Cooney-Cross and Caitlin Foord on deck, were another side to win 2-0 thanks to goals from Laia Codina and Stina Blackstenius.
Australian Mary Fowler played in Manchester City's 3-1 victory over WSL strugglers Leicester.
Leila Ouahabi and Kerolin put the home side two up at half-time and Khadija Shaw added a third just before the half-hour mark. Nelly Lasova scored a consolation for Leicester eight minutes from time.
Sunderland are the only non top-flight side left in the competition after beating fellow WSL 2 outfit Portsmouth 2-0.
Jenna Dear and Emily Scarr both scored late in the first half, while Portsmouth ended the match with 10 players after Scarlett Williams was sent off.
9°C