Derek Riordan netted a ninth-minute opener and hit the bar with a free-kick soon afterwards and Colin Nish had a second-half effort ruled out for offside as Hibs were again frustrated and booed off by their own supporters.
Accies troubled the hosts on the break and were worthy of Marco Paixao's 22nd-minute equaliser following Nigel Hasselbaink's strong run.
Hibs, unchanged following last week's 1-1 draw with Inverness, were without a home win since March 6 and were last week jeered off the pitch by the Easter Road faithful.
Accies, seeking their second win of the season and with the worst defensive record in the league, were welcome opposition.
Hibs defeated Billy Reid's side 5-1 in Edinburgh in January and the visitors were without a win at Easter Road since the 1986/87 season.
Marco Paixao blazed high and wide after eight minutes before Riordan, who gave Hibs an early lead against Caley Thistle, put the hosts in front at the other end.
Riordan sneaked in behind the Accies defence to intercept Marco Paixao's mis-directed back pass and, after being initially denied while trying to round Tomas Cerny, beat the Hamilton goalkeeper at the second attempt.
Cerny was beaten again three minutes later, but Riordan's 25-yard free-kick hit the bar and bounced down a yard in front of the line.
Riordan was denied by the Accies stopper after 19 minutes following Liam Miller's strong run down the left before Sol Bamba cleared Flavio Paixao's header at the other end.
Hamilton levelled after 22 minutes following a direct run by Hasselbaink - nephew of former Holland international Jimmy Floyd Hasselbaink - which was only partially stopped, allowing Marco Paixao to sweep in the equaliser.
Nish, Edwin de Graaf and Riordan combined soon after but the latter's cross was too high for the onrushing Miller, who could only head over.
Midfielder David Wotherspoon, who looked promising in the early stages, then limped off after 31 minutes to be replaced by Daniel Galbraith.
Kevin McBride and Jonathan Grounds then combined down the right and Riordan missed from close range.
Hasselbaink and Marco Paixao linked well together again as half-time approached, but the latter could not get a shot away.
Hamilton could not trouble Hibs goalkeeper Mark Brown despite a free-kick - for a foul which saw De Graaf booked - and two corners in the opening three minutes of the second half.
Hibs were struggling to keep possession, but thought they had a second only to be denied by the referee's assistant after Nish was ruled offside when tucking in Galbraith's cross.
Hamilton broke quickly and Michael Hart stopped Hasselbaink as the Dutchman attempted to get a shot away.
Marco Paixao then missed a gilt-edged chance when through one-on-one with Brown, firing wide from 12 yards under pressure from the Hibs defence.
Nish went to ground under the attention of Mark McLaughlin, but referee Euan Norris ignored muted appeals for a penalty.
Riordan then shot wide before Cerny saved with his legs from the forward, who fired in left-footed after McBride's lofted pass.
Valdas Trakys came on for his debut with 14 minutes remaining, replacing Nish, but had little opportunity to impress in a fragmented game.
Riordan fired wide having already been flagged offside as Hibs were left frustrated at home once again.