Rangers moved above Aberdeen in the SPL table on Tuesday, but Celtic remain the runaway leaders.
Steven Pressley made his debut for Celtic as the SPL leaders were 2-0 winners at home to Kilmarnock.
Defender Darren O'Dea scored the opener (38) after Shunsuke Nakamura's free-kick was not cleared.
Nakamura provided a late second for Aiden McGeady to coolly finish past Graeme Smith and give Gordon Strachan's men the perfect start to 2007.
Rangers claimed a narrow 1-0 success over Motherwell in a feisty encounter at Fir Park.
Both sides could have easily found themselves ahead before Rangers were handed the chance to take the lead from the penalty spot.
Dado Prso was brought down by Motherwell keeper Graeme Smith and Kris Boyd made no mistake from the spot, slotting home into the bottom corner (70).
Both sides were reduced to ten men minutes later after a goalmouth scramble resulted in a tussle in the Rangers penalty area.
Marc Fitzpatrick and Prso were both shown straight red cards, but Paul Le Guen's side held on for the points.
Hearts were away winners in the early kick-off at Dunfermline, with Michal Pospisil netting from Bruno Aguiar's corner after 15 minutes.
Aberdeen slipped to third place after a 0-0 draw with Hibernian at Easter Road.