"I was pleased with my team and it looks like we're getting to grips with this league," said Blackpool coach Ian Holloway, whose side were promoted from the second tier last season.
"It's wonderful to see us play that well against Everton."
The result leaves both sides on 14 points, with Everton falling a place to 10th in the Premier League table and Blackpool also dropping a place to 11th.
"In the last 10 to 15 minutes Blackpool put us under pressure," said Holloway's Everton counterpart, David Moyes.
"We showed a lot of character but we started badly. We made the wrong decision too many times."
Having secured their first top-flight home victory since 1971 with a 2-1 defeat of West Brom on Monday, Blackpool began the game in assured fashion and took the lead in the 10th minute.
Mikel Arteta was penalised for hacking down Charlie Adam just outside the penalty area and Welsh international full-back Eardley, who was celebrating his 22nd birthday, curled the resulting free-kick past Tim Howard.
The visitors did not have to wait long for an equaliser, with only three minutes having elapsed when Cahill met Aiyegbeni Yakubu's left-wing cross to power a header past Matt Gilks in the Seasiders' goal.
Everton began to assert themselves with more conviction thereafter.
Cahill saw a first-time effort deflected by Yakubu into the arms of Gilks, while Irish youngster Coleman placed a shot narrowly off-target after cutting in from the flank.
It was the hosts who struck first in the second half, however, as Eardley's international team-mate Vaughan slammed home following a goalmouth scramble in the 48th minute.
As in the first period, however, Blackpool were unable to protect their lead and barely two minutes later Coleman seized on Stephen Crainey's weak header before squeezing a shot beneath Gilks to restore parity once again.
Adam spurned a chance to put Blackpool ahead for a third time when he shot wide just after the hour, before Gilks saved a scuffed effort from Steven Pienaar after the Toffees midfielder had been set free by Cahill.
Pienaar then created a good opportunity for substitute Louis Saha, but the French striker fired wide from a decent position.
Amid pouring rain the game opened up in the closing stages, but despite Adam drawing a fine save from Howard and Marlon Harewood seeing a goal chalked off for offside, Blackpool were unable to muster a winner.
Source: AFP Global Edition