The defending WSL champions set the tone from kick-off with Aggie Beever-Jones forcing a save from Courtney Brosnan with just 37 seconds on the clock.
The Blues forward then notched the opener in the 14th minute and the chances continued to flow with Kadeisha Buchanan, Erin Cuthbert and Guro Reiten all going close.
Scot Cuthbert made certain of her second opportunity two minutes before half-time, guiding the ball into the bottom corner after picking the pocket of Everton defender Veatriki Sarri.
Chelsea went into the break with a three-goal advantage after Reiten stretched to turn in at the back post in added time.
The visitors continued to press for further goals and eventually got them late in the second half after twice being denied by the woodwork.
Substitute Wieke Kaptein smashed in the fourth with eight minutes left and Ashley Lawrence had a tap-in just a minute later to wrap up a high-scoring triumph.
Chelsea moved above Brighton into second spot in the WSL, a point adrift of leaders Manchester City with a game in hand, while Everton remain bottom on two points after six games.
Chelsea's last defeat in the Women's Super League came on 1 March against Liverpool
