The Hoops had thrashed the administration-hit visitors 7-0 in their Scottish Cup clash at Tynecastle at the beginning of the month - with Kris Commons scoring a hat-trick - and Jambos boss Gary Locke was keen to ensure there would be no repeat.
The Gorgie side were set out to keep a clean sheet although goalkeeper Jamie MacDonald had to make several saves in the first half, the best from a Joe Ledley header.
However, the Hoops remained patient after the beak and got their reward when Commons scored in the 63rd minute with a powerful drive and the 30-year-old also cleared off the line near the end before James Forrest, on for Nir Biton for the start of the second half, grabbed a second at the end.
While Celtic's inexorable march to the title continues steadily, there seems no end to the struggle of the Gorgie club to avoid relegation, despite a valiant effort.
Aberdeen survived a spirited second half showing from Inverness to move up to third in the Scottish Premiership after edging a seven-goal thriller in the Highland Capital.
The Dons raced into a 4-0 lead at the interval courtesy of two Barry Robson goals - one of which was the opener from the penalty spot - Peter Pawlett and Niall McGinn.
The hosts produce a more robust display after the break with Billy McKay scoring twice and Graeme Shinnie on target, but it ultimately proved all in vain as Aberdeen ran out winners over the Caley Jags for a second time this season.
Dundee United continued their recent run of fine form thanks to a hard-fought 1-0 win over lowly Ross County at Tannadice.
Gary Mackay-Steven's 69th minute winner was enough to give them the three points and leave second-bottom County languishing near the foot of the the table.
Loan pair Henri Anier and Lionel Ainsworth showed their worth to Motherwell as they bagged the goals in a 3-0 victory over St Mirren.
Anier took his tally for the season to seven with emphatic finishes in each half and Ainsworth coolly finished off a well-worked move in between as Motherwell secured their 10th Scottish Premiership win and their first Fir Park victory over St Mirren for three years.
Kris Boyd's second-half winner allowed Kilmarnock to pinch ninth place from opponents Partick with a 2-1 win at Rugby Park.
The former Scotland striker struck 20 minutes from time to take his tally to nine for the season and continue his impressive goal-every-two-games strike rate.
In-form teenage winger Chris Johnston contributed his third goal in four games for the opener after 41 minutes, but the hosts were pegged back soon after the break as Kris Doolan levelled for Thistle.
However, Partick - who have not won since beating Inverness on October 20 - paid the price for Steven Lawless' incredible empty-net miss when Boyd touched home from Jackson Irvine's shot to confirm the three points.
St Johnstone battled for over an hour with 10 men to claim a well-deserved point at Hibernian.
Just seconds after replacing the injured Murray Davidson, former Hibernian midfielder Paddy Cregg was shown a straight red card for a wild two-footed challenge on Paul Cairney.
Despite their numerical advantage, the hosts struggled to break down a rigid Saints rearguard.
Hibernian enjoyed a sustained period of pressure at the start of the second half that had the visitors at full stretch but they failed to convert that dominance into a goal.
And referee Alan Muir was not interested in injury-time appeals for a penalty after the home team's striker James Collins appeared to be bundled over by Brian Easton.