Rangers saw title rivals Celtic extend their lead atop the SPL to five points after Ally McCoist's side stumbled to a 1-1 home draw against Aberdeen on Saturday.
Needing a win to keep pace with their cross-city rivals, Rangers made life difficult for themselves after they fell behind to Kari Arnason's second half strike, and Maurice Edu's equaliser was not enough as the Gers were held to a frustrating draw.
Nikica Jelavic had a number of good chances to score as the home side failed to make a first half breakthrough. The Dons had a great chance of their own when McGregor fumbled a corner and Carlos Bocanegra cleared off the line, but the visitors were ahead after 63 minutes when Arnason met a Chris Clark ball and curled past the Rangers goalkeeper.
The Scottish champions were back on level terms just four minutes later when the ball broke for Edu to rifle high into the top corner of the net - but both Edu and Kyle Bartley wasted further opportunities to complete the Gers comeback as their recent difficulties continued.
A tactical reshuffle from manager Neil Lennon proved crucial as Celtic claimed an important 2-0 win over St Mirren in the day's early kick-off.
Celtic, looking to increase their slim advantage over Rangers in the SPL title race with a victory, initially found it difficult to gain the upper hand at St Mirren Park, as the hosts enjoyed the majority of openings.
But Lennon's decision to take off Georgios Samaras for Kris Commons and Ki Sung-Yueng for Anthony Stokes midway through the second half reaped dividends, as James Forrest opened the scoring with a precise drive ten minutes later, before Scott Brown killed off the contest with a 20-yard strike - assisted by Commons - with just a few minutes remaining on the clock.
In a game which was spoiled by the wind, Celtic's best effort in the first-half was Gary Hooper's long-distance strike which St Mirren goalkeeper Craig Samson saved.
Celtic keeper Fraser Forster was also forced to make a string of saves, the best being from former Parkhead midfielder Paul McGowan.
A stunning late winner from Francisco Sandaza secured a 3-2 win for St Johnstone over Hibernian after a breathless encounter at Easter Road.
Lee Croft opened the scoring in the first half with a fine low finish, but that lead was cancelled in the second period through a Leigh Griffiths penalty. Parity lasted mere seconds, with wasteful defending allowing Liam Craig to restore the Perth side's lead.
Hibs, displaying admirable character, made it 2-2 through Callum Booth's neat finish, but the excellent Sandaza - whose future at the club remains in some doubt - found space to fire home a superb late winner.
Dunfermline recorded their first win in almost three months as they hammered Kilmarnock 3-0 at Rugby Park. Andrew Barrowman opened the scoring with five minutes remaining in the first half and Joe Cardle doubled the visitors' lead on the hour mark.
With three minutes remaining Liam Buchanan added a third to ensure Dunfermline's first ever Scottish Premier League victory at Rugby Park.
Elsewhere, Hearts were beaten in disappointing fashion by Inverness Caledonian Thistle - the home side having Shane Sutherland's strike shortly after half-time to thank as they edged a 1-0 victory - and Motherwell left it late to claim a dramatic 1-1 draw with Dundee United.
United looked to comfortably on course for victory as they clung onto the lead given them by Stephen Craigan's own goal after 30 minutes, but Michael Higdon popped up inside the box to convert Henrik Ojamaa's cross with just a handful of minutes remaining.