England star Mead’s double added to Vivianne Miedema’s opener, with more than 8,000 fans lapping up an exciting encounter in north London.
Erin Cuthbert had Chelsea level at 1-1 at the break as boss Emma Hayes racked up her 250th match at the Blues’ helm.
Mead struck twice in 11 second-half minutes however to turn the tide, and the hosts held on despite Pernille Harder’s effort teeing up a tense finale.
Brighton jumped to second in the embryonic table thanks to a 2-0 win over 10-woman West Ham.
The Hammers had Hawa Cissoko sent off just past the half-hour mark, and never recovered from that dismissal.
Inessa Kaagman’s penalty handed the hosts the lead, and Lee Geum-Min found the net before half-time as Brighton effectively settled the contest before the interval.