Aberdeen and St Johnstone joined Celtic in maintaining their perfect start to the season but Rangers were held at home.
The Dons, who finished runners-up last season, beat Dundee 2-1 at Pittodrie to make it three league wins from three and stay tied on points with the champions and the Saints at the top of the fledgling table.
Stevie May scored the opener for the hosts when he made a good run off the post to find space and head past goalkeeper Scott Bain from Greg Tansey's corner.
Former Sutton striker Roarie Deacon notched the equaliser in the 53rd minute when he drove forward into the box and sent a low shot through Joe Lewis' legs but May produced again when he fired a rocket past Bain after Graeme Shinnie's shot was blocked.
Brendan Rodgers' Hoops - top of the early standings on goal difference - made changes after their midweek Champions League play-off thrashing of Astana but still eased to a routine 2-0 win over Kilmarnock.
A smart finish just before the break by winger James Forrest, taking over as main striker from Leigh Griffiths, and a late strike by midfielder Callum McGregor meant Celtic remain unbeaten this season in all competitions.
Second-placed St Johnstone also sealed another three points by beating Partick Thistle 1-0 thanks to Michael O'Halloran's strike just after the half-hour mark.
It was O'Halloran's fourth goal in three league games as the on-loan Rangers forward continued his strong start to the season.
Hibernian slipped out of the top three after they were beaten 3-1 by Hamilton - the side who doomed them to relegation on their last visit to Easter Road in 2014.
Rakish Bingham broke the deadlock with a 52nd-minute penalty after midfielder Greg Docherty was fouled just inside the Hibs box before Ali Crawford set up Louis Longridge for the second on the counter-attack.
Bingham added a third for Accies to seal the win in the 88th minute before Anthony Stokes' late consolation for Hibs.
Motherwell claimed their first league win of the season with a 2-0 victory against 10-man Ross County.
Richard Tait found himself with plenty of room inside the box before coolly slotting past keeper Scott Fox for the opener before Louis Moult scored the second from the penalty spot after he was brought down by defender Kenny van der Weg in the box.
Dutch defender Van der Weg was sent off the for challenge leaving County to play the last 15 minutes with 10 men.
Meanwhile, Rangers drew a blank with Hearts at Ibrox to remain in sixth place in the league standings.