O'Neill enjoyed great success during a five-year spell in charge of the Glasgow giants between 2000 and 2005 and was appointed interim boss on Monday after Brendan Rodgers resigned amid acrimonious relations with the club's board.
The 73-year-old had an immediate impact as Celtic shrugged off an injury crisis to storm to their biggest league victory of the season.
Johnny Kenny struck twice in a 10-minute spell just before half-time to settle the hosts after a tumultuous week.
Rodgers stepped down after back-to-back league defeats at Dundee and Hearts, but was accused of "divisive, misleading and self-serving" behaviour by Celtic's largest individual shareholder Dermot Desmond.
Further goals from Benjamin Nygren and Sebastian Tounetki allowed O'Neill the chance to rest a number of key players for the final stages ahead of Sunday's League Cup semi-final showdown against Rangers.
Hearts' six-game winning run came to an end in Paisley as Derek McInnes' side were fortunate to maintain their unbeaten record in the league.
Twice St. Mirren led through Dan Nlundulu and Miguel Freckleton.
But the game swung on a controversial VAR intervention to rule out a second for Freckleton that would have put the Buddies 3-1 up.
Instead, Hearts, who had levelled in the first half through captain Lawrence Shankland, equalised 20 minutes from time thanks to top scorer Claudio Braga.
Pierre Landry Kabore thought he had snatched all three points for Hearts late on but this time a VAR review when St. Mirren's way for an offside against Oisin McEntee in the build-up.
Rangers climbed up to third and within 11 points of the leaders thanks to Jack Butland's late penalty save in a 1-0 win at Hibernian.
Danilo's fine strike from outside the box after just five minutes proved to be decisive.
But Danny Rohl's side needed Butland to deny Jamie McGrath from the spot five minutes from time to secure victory.
Aberdeen won 1-0 at Kilmarnock to ease the pressure on manager Jimmy Thelin.
Motherwell leapfrogged Dundee United into fifth with a 2-0 win at Fir Park.