A late strike by substitute Teddy Jenks gave Aberdeen a narrow 1-0 cinch Premiership win over struggling St Johnstone at McDiarmid Park.
Ross County picked up a second win over Dundee this season in an enthralling contest in Dingwall which they edged 3-2 to move off the bottom of the table.
Livingston made it two cinch Premiership wins in a row with a 1-0 victory over Dundee United at Tannadice.
Scott Brown went off injured on his return to Celtic Park after his successor as Hoops captain, Callum McGregor, netted a fortuitous winner against Aberdeen.
Giovanni van Bronckhorst made the perfect start to life as Rangers boss in the Scottish Premiership as he oversaw a 3-1 win over Livingston.
Stephen Kingsley scored a sublime free-kick as Hearts ground out a hard-fought 2-0 victory over 10-man St Mirren at Tynecastle.
Ten-man Ross County rescued a last-gasp point with a stoppage-time leveller to deny Dundee United the chance to edge past Celtic into third spot.