The Gers wasted precious little time in breaking the deadlock when Kirsty Howat struck inside three minutes, adding to their advantage from the penalty spot in the second period through Katie Wilkinson.
Saiorse Noonan restored hope for the away side from 12 yards, before Celya Barclais slammed home an equaliser with five minutes remaining.
It was the first Old Firm instalment of the campaign for both sides, with the fixture rescheduled owing to the involvement of either side in UEFA Champions League qualifying.
Although typically cagey affairs, it was Rangers who were rampant from the outset as they immediately put the away side under pressure.
A Lizzie Arnot free-kick from the left-hand side found its way back to the winger whose return delivery was turned behind by Emma Lawton at the far stick.
It was a sign of intent from Jo Potter’s side and they were rewarded for their early endeavour inside three minutes when Kirsty Howat blew the roof of Broadwood Stadium.
The ball seemed to ping across the Celtic penalty area from a Gers corner after it was flicked on at the near post by Katie Wilkinson, allowing Howat to stride onto the dropping ball and smash an unstoppable volley beyond Kelsey Daugherty.
It was no more than the hosts deserved, going close seven minutes later when Wilkinson fashioned a dangerous half-volley towards goal on her left side which was tipped over by Daugherty at full stretch.
The hosts thought they had doubled their advantage moments later when a delivery from the left-hand side was glanced into the back of the net by Tessel Middag, but the linesman adjudged that Rio Hardy was standing in an offside position and had infringed on the line of sight of the away side’s goalkeeper.
Celtic had been reduced to very little and they were spooked by the speed of Rangers’ play, although they briefly threatened when Morgan Cross put Eddie under pressure and scooped an effort into the grateful arms of Vic Esson.
Rangers were deriving particular joy when pressing the visitors high up the pitch, pouncing on moments of slackness and attacking quickly through the energy of Hardy, Arnot and Wilkinson.
Down the other end, Cross continued to prove the away side’s brightest spark, hitting the byline three minutes before the interval and flashing a wicked delivery across the face of goal which was defended smartly by the backtracking Brogan Hay.
The Gers emerged for the second-half with a renewed intent, causing the visitors issues when a deep delivery from Arnot reached Wilkinson but the English forward could only head off target under pressure.
Hardy was next to test her luck when she displayed tremendous hold-up play on the edge of the penalty area, moving smartly onto her left-hand side before forcing Daugherty into a relatively comfortable stop.
Clear-cut opportunities were in short supply for either side, which was music to the ear of the hitherto untroubled Gers rearguard.
And that proved the cue for Rangers to tighten their grip on the contest on the stroke of the hour-mark and leave the visitors with a mountain to climb.
Strong hold-up play from Wilkinson allowed her to advance towards goal and pick a pass out wide to Arnot, whose return delivery struck the arm of Lawton and, after a moment of hesitation, the referee duly pointed to the penalty spot.
Wilkinson assumed spot-kick duties and dispatched confidently into the bottom corner to bring Broadwood to its feet for the second time in the evening.
However, the visitors reduced the arrears with 23 minutes remaining when Lawton, penalised just minutes earlier, went down under contact from Nicola Docherty. Noonan stepped up from 12 yards and sent Esson the wrong way to hand the away side a lifeline.
Jo Potter turned to her substitutes bench in the final quarter of an hour as Mia McAulay replaced Hay, with Esson called into action when she saved with her feet from Lawton.
Celtic then equalised to salvage a point with five minutes remaining when Barclais slammed home at the back post.
RANGERS: Esson, Docherty, Eddie, Hill, Middag, Hay (McAulay, 77), Howat, Hardy (Devlin, 71), Arnot, McLoughlin, Wilkinson
Subs: Fife, Rafferty, Bell, Ross, Austin, Lafaix, McLeary
CELTIC: Daugherty, Ross (Barclais, 82), Gallacher (Cavanagh, 45), Agnew (Noonan, 66), McGregor, Clark, Cross, Hayes, Ashworth-Clifford (S. Carstens, 82), Lawton, Costa
Subs: Rodgers, Richardson, M. Carstens, Munoz, McAneny