Richard Offiong's ninth-minute goal looked to have given Accies a rare victory but Dundee United finally got the equaliser they sought so frantically deep into time added.
Simon Mensing was controversially dismissed with eight minutes remaining after an off-the-ball altercation sparked by Craig Conway's push on the prostrate James McArthur.
And the visitors paid the price for a lack of numbers in defence as Conway's corner caused confusion and Easton appeared to get the last touch on John Daly's effort in a crowded goalmouth.
United manager Craig Levein, who reportedly turned down advances from Watford recently, made only one enforced change as he attempted to return his side to winning ways against bottom side Hamilton.
The Tannadice sides' 10-game unbeaten run was brought to an end with a 2-0 defeat away to Kilmarnock last weekend but Levein's measured response was to bring in Daly for the suspended Roy O'Donovan up front.
And he will at least have been happy to see his side avoid the defeat they looked to be heading for until four minutes into injury time.
Hamilton were also forced into an alteration because of suspension, with defender Martin Canning sitting out the match after his red card in the controversial 2-1 defeat to Celtic last weekend.
David Elebert was a straight swap for the former Hibs and Gretna stopper and the visitors defended stoutly until succumbing late on.
And after some tentative early sparring, Accies got the early breakthrough they wanted as they took the lead after only eight minutes.
James McCarthy won the ball 25 yards out and fed Mensing who looked offside in space wide on the right.
His low centre was perfect for Offiong and the striker made it two goals in as many games with an astute finish from 10 yards.
The goal stunned the home side but they came close to an equaiser 10 minutes later as Conway's inswinging corner caused havoc in the Accies goalmouth.
Keeper Tomas Cerny flapped at the flag-kick but was helped out by Trent McClenahan on the line and the subsequent centre was headed just wide by Daly.
The game burst to life in the 36th minute when Neil's corner struck the outside of the near post and Mensing's shot with the outside of his right boot swerved wide.
A minute later, Cerny was called into action at the other end as Lee Wilkie's cute back heel allowed Scott Robertson to cut back for Darren Dods to fire in a shot.
United knew they needed an improved second-half display if they were to avoid back-to-back defeats for the first time since plunging to the foot of the table in September.
However, they continued to struggle to create anything against Hamilton's resolute rearguard, their sturdy central defenders coping easily with too many long balls forward from the home side.
Offiong had an opportunity to virtually sew up the points in the 63rd minute as Accies launched a lightning break.
McArthur robbed Robertson on the edge of his own area and sprinted forward before feeding Mensing but Offiong screwed his centre horribly wide from the edge of the area.
United almost grabbed the equaliser when Paul Dixon took a free-kick quickly to set up Willo Flood on the right side of the box but Cerny did enough to put off the midfielder and his chipped shot hit the side netting.
Accies were then reduced to 10 men in controversial circumstances with eight minutes remaining as Mensing received a second yellow card for an off-the-ball push on Conway, who himself was guilty of a push on McArthur.
Wilkie's shot was deflected wide by McArthur with five minutes remaining as United threw everything at the visitors in the closing stages.
And four minutes into injury time they finally got the goal they wanted as Easton swung at Conway's corner under a challenge from Daly and appeared to knock the ball into his own net.