Having won just one of their previous 30 games, the Bombers finally played with a sense of urgency to give Solomon his first win in his 10th match as a caretaker coach, which includes three at Gold Coast in 2017.
Leading at every break, Essendon gave up their advantage twice in a frantic final term but hit back through clutch goals to Sullivan Robey and Peter Wright.
With a wildcard spot still up for grabs, the Giants desperately tried to reclaim the lead in the dying stages, but Essendon hung on for a famous win - 10.7 (67) to 8.16 (64) amid scenes of delirium in front of a small, but vocal crowd at Marvel Stadium.
It was Essendon's first win since beating Melbourne in Gather Round in Adelaide on April 11, while they hadn't won a game in Victoria since May, 2025.
The Bombers, who were ravaged by Brisbane last Sunday and had lost 12-straight matches, were given virtually no hope of matching it with the red-hot Giants.
"It's a bloody good feeling," Solomon said.
"Our footy club's been on its knees for a period of time, and the footy world's jumped on that, and they enjoy us sitting at the bottom.
"We've felt that, and we don't like that, so to push back a little bit and get one win, albeit one win, I'm just really happy for these players."
The result continued GWS's baffling trend of struggling against lower-ranked opposition whilst also dismantling last year's grand finalists Brisbane and Geelong, and rampaging ladder-leaders Fremantle, amid their previous seven games.
As well as the Bombers, GWS have dropped matches to St Kilda (twice) and West Coast.
"It was incredibly disappointing," Giants coach Adam Kingsley said.
"The messaging around our consistency, our ability to perform against every team in the competition, not just those who were above us."
In a further concern for the Giants, they lost captain Toby Greene to a serious-looking quad injury in the third quarter that will almost certainly mean he misses the Sydney derby against the Swans next Saturday.
Further delighting the home crowd, former Essendon forward Jake Stringer endured a horror match in front of goal to finish with 0.7 on a wayward night for the Giants.
The only concern for Essendon was young star Nate Caddy, who was sent to hospital due to an elevated heart rate.
Caddy, who recently re-signed until the end of 2031 in a massive boost for the battling Bombers, didn't return to the ground after quarter-time.
Solomon revealed Caddy had been able to leave hospital, but would undergo further tests during the week.
"To do it without him is sad in one instance, but it's also a pretty super effort from this group," Solomon said.
The result could prove costly for GWS, who would have jumped into 10th and a wildcard spot, had they beaten the Bombers.
It also lifted Essendon to 17th, sending Richmond to the bottom of the ladder.
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