The Redcliffe side trailed 10-0 after 19 minutes before scoring five consecutive tries in front of 24,728 fans to notch an eighth-straight win at Suncorp Stadium on Friday.
Victory pushed Kristian Woolf's men level on 36 points with the third-placed Warriors, still to play on Saturday, with two rounds to play before the club's first finals appearance.
Now two wins clear of Cronulla and Newcastle (32 points), both yet to play this round, the Dolphins can sew up a top-four berth with a win over Sydney Roosters next Saturday.
"That was a tough game for us ... you're expected to win, a big game next week against the Roosters, so it's hard not to look ahead a little bit at times," Woolf said.
"There's a bit to learn for us. We need to be better next week, better in finals, but we got a win and there's plenty of good things to take away.
"Sitting in the top four, it's all in our hands and we'd love to play as many finals as we can here."
Herbie Farnworth scored twice, halves Kodi Nikorima and Isaiya Katoa combined well while Selwyn Cobbo was powerful out of defence and Max Plath dynamic in another bench cameo.
But the Dolphins, who have led after 20 minutes just five times this season, had to overcome another slow start when Eels five-eighth Ronald Volkman took off from dummy half and scored.
The visitors, thanks to a series of high tackles from Dolphins centre Jack Bostock, led 10-0 when Will Penisini somehow offloaded in contact and set up Brian Kelly.
The Dolphins' response felt inevitable though and, with Katoa balancing his kicking and running game, found joy off a scrum when Farnworth wedged open a half-gap to score.
A set restart immediately gave the hosts another chance, they went from right to left and Nikorima eyed the overlap that finished in a Cobbo try.
It was a third Dolphins try in 11 minutes when Jamayne Isaako, contentiously after a lengthy review, avoided a strip attempt to ground a try after a brilliant Bostock assist.
Cobbo thought he had another on halftime when he volleyed a loose Farnworth pass and picked off the pin-ball rebound off an Eels player to score, only for the pass to be ruled forward.
Instead it was Isaako on the double as the winger stepped back inside to finish another bit of good work from his centres and halves and make it 22-10 early in the second half.
Kelma Tuilagi finally ended the run of Dolphins tries when he was first to a loose ball in-goal that a diving Nikorima failed to kill.
But Farnworth ensured the hosts had the final say, racing 85 metres after picking up a loose pass to nab his second.
Bostock and Thomas Flegler, for his hip-drop tackle late in the game, were placed on report.
Eels coach Jason Ryles was furiously opposed to the bunker's decision to award the Isaako try but admitted his young side had been taught a lesson.
"Fight and effort only gets you so far and we hung in for a long period," he said.
"They're a well put together, physical, mature footy team and we've got a heap of kids out there at the moment learning their trade."
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