Paxman had 24 disposals and Kate Hore kicked three goals as the Demons posted a convincing 7.8 (50) to 1.3 (9) victory at Casey Fields on Sunday.
It was the Dees' fifth consecutive win and kept them within touching distance of ladder leaders Brisbane, with only percentage points separating the two with one home-and-away round left.
Another win over lowly West Coast on Saturday could be enough for Melbourne to overtake the Lions - who host Collingwood on Friday night - and snare the minor premiership.
The tight finish follows another strong defensive showing from the Demons, who have held opponents to an average of 14.2 points per game in the past five weeks.
Essendon star Madison Prespakis tried to lift her side and had 16 first-half disposals but was restricted by Shelley Heath after the main break.
Melbourne had plenty of contributors. Hore was dangerous throughout and Paxman starred from the outset, finishing with one goal and six tackles.
The veteran led a midfield unit that was also well served by Olivia Purcell (23 disposals), Tyla Hanks (19) and Eliza West (15).
Libby Birch stood tall as part of a back six that didn't have a lot of work to do, while Alyssa Bannan kicked two goals.
Essendon captain Bonnie Toogood worked hard at both ends of the ground and Catherine Phillips kicked their only goal.
The Bombers are out of finals contention but will look to end their debut season on a high against fellow expansion side Port Adelaide on Sunday.
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