In Arctic conditions, Gers took the lead on 81 minutes through a Brian Easton own-goal before Ross Callachan levelled matters deep into stoppage time.
Boss Steven Gerrard named three changes to his side from the team which defeated St Johnstone 1-0 in midweek Bongani Zungu, Glen Kamara and Cedric Itten came in to the starting XI in place of Ryan Jack, Steven Davis and Kemar Roofe.
Some light snow was falling as the teams came out onto the New Douglas Park pitch, but it was to be the biting, blustery wind that would be the biggest obstacle weather-wise to overcome this afternoon.
Gers had much of the early possession, and indeed, Ross Callachan was booked with less than a minute on the clock for a pretty dangerous challenge on Connor Goldson.
Accies’ Bruce Anderson and Gers’ Ianis Hagi exchanged shots from distance which went wide, while Joe Aribo had a header on the end of a James Tavernier free-kick go over.
Aribo then showed super skill in the middle of the park to work an angle for a 25-yard shot which went just wide, while Allan McGregor made a good block from Anderson when Gers were caught trying to play out from the back.
Goalkeeper Ryan Fulton did well to clutch a Connor Goldson header on the end of a Tavernier corner, while Tavernier saw a 25-yard free-kick go just over as the teams went in level at the interval.
Gers opened the second half with a renewed energy, and Ryan Kent struck the side netting with a wicked effort within a minute of the restart, before Aaron Martin denied the winger with a super block when Itten put him in.
Jamie Hamilton then blocked a Kent effort on the end of a Tavernier cross, before a superb, double save from McGregor from Scott McMann and then Callachan prevented Hamilton from taking the lead against the run of the second half play.
Fulton gathered another Aribo effort from outside of the area, while McGregor saved from Anderson again, this time with his feet.
Kent fired wide when a ball from Ryan Jack found its way to him in the area, wile McGregor was forced into action again, this time to deny Callachan from a 25-yard, powerful free-kick.
Gerrard made a double sub on 78 minutes, handing Scott Wright a debut and also bringing on Steven Davis, and Davis had the desired impact three minutes later with a stunning piece of play to open up the home defence.
He threaded a sublime ball down the left for Borna Barisic to receive in space, before the Croatian international burst into the box.
He crossed and got it by goalkeeper Fulton, and before the incoming Tavernier could finish, the ball deflected off Brian Easton and landed in the back of the net.
The moment of quality from Davis was exactly what the visitors were after, but deep into stoppage time, Accies levelled.
McGregor made a fine initial save from Callachan, but he pounced on the rebound to leave matters all-square.
RANGERS: McGregor, Tavernier, Goldson, Helander, Barisic, Aribo, Zungu (Jack, 59), Kamara, Hagi (Wright, 78), Kent, Itten (Roofe, 66).
SUBS NOT USED: McLaughlin, Bassey, Simpson, Patterson, Balogun.
HAMILTON ACADEMICAL: Futon, Odoffin, McMann, Easton, Hamilton, Anderson, Ogkmpoe, Trafford (Hughes, 71), Martin, Hodson, Callachan.
SUBS NOT USED : Gourlay, Stanger, Mimnaugh, Winter, Moyo, Munro, Slaven, Smith.