Neil Lennon's men had been thrashed 6-1 in their final Champions League Group H game in the Nou Camp on Wednesday night.
Teemu Pukki had borne a lot of the brunt for that defeat but the Finnish striker made amends by scoring the winner in the 28th minute from close range to extend Celtic's unbeaten run in the league to 15 games and keep them on course to retain their title.
Clinical Billy McKay took his goal tally for the season to 15 in the 2-0 victory at Hearts that handed John Hughes his first win as Inverness boss.
A scrappy contest, played in abominable conditions in Edinburgh, was effectively decided when McKay showed typical intelligence and composure to find the opening goal on the hour.
The visitors' lead was doubled with a scintillating counter-attack, with Marley Watkins surging from the halfway line before finding McKay, who slotted home his second of the game.
Dundee United were 4-1 winners against Kilmarnock.
Second half goals from Keith Watson, Stuart Armstrong, Ryan Gauld and David Goodwillie saw the visitors overcome 10-man Killie.
A late consolation goal from Kris Boyd allowed the former Rangers striker to claim his 175th top flight goal and overtake Henrik Larsson's haul.
Barry Robson netted direct from a corner as Aberdeen continued their resurgence with a comfortable 2-0 win over St Mirren to stay in touch with Inverness and Dundee United in the race for second spot.
Robson's second half strike came after Scott Vernon had given the Dons the lead, taking full advantage of a mistake from Marc McAusland.
Two goals from John Sutton got Motherwell back to winning ways as they beat Ross County 2-1 at the Global Energy Stadium.
Sutton struck twice in the first half hour as the visitors dominated, but a spirited second-half showing from County saw them reduce the deficit through Melvin De Leeuw.
Partick Thistle's clash with St Johnstone was abandoned at half-time due to a waterlogged pitch at Firhill.
Referee Kevin Clancy called the match off after a goalless first half.