The Bombers appeared destined to rue their inaccuracy when the Eagles claimed a one-point lead late in the piece.
But with 50 seconds left, the home side surged forward and Georgia Gee picked out lifelong Essendon fan Alexander, who kicked truly to deliver a 4.7 (31) to 4.2 (26) victory.
"I don't think the adrenaline will leave my body for a while now," Alexander told Fox Footy.
"It's about time I turned up and did something. You can have a rubbish game and come in in the end and still get your moment in footy. So very happy.
"We needed that (win) and it's only gonna make us stronger."
The Bombers move to 2-0 but the win came at a cost, with Van De Huevel suffering a knee injury in the second term.
Essendon midfielders Georgia Nanscawen (24 disposals), Amy Gaylor (22) and Maddy Prespakis (22) starred while skipper Bonnie Toogood (2.3) had her moments.
Eagles gun Ella Roberts (21 disposals) and veteran Emma Swanson (20) were excellent, while Kayla Dalgleish kicked two goals.
Toogood drew first blood inside the opening minute, before Abbygail Bushby levelled the scores following a 50-metre penalty just before quarter-time.
Dalgleish put West Coast in front midway through the second term, and they led by five at halftime.
Toogood missed two consecutive golden chances but then nailed her most difficult shot of the quarter to deliver a four-point lead.
Gee nudged Essendon out to a 10-point lead early in the final term, before Dalgleish responded with a running goal.
Essendon spurned big chances and the visitors made them pay, with Kellie Gibson strolling into an open goal to deliver the lead.
But Gee and Alexander's late combination saved the day.
The Bombers now face Richmond in Darwin next Friday, while West Coast (1-1) play St Kilda at RSEA Park on Saturday.
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