Rangers were rocked by Hibernian at Ibrox as Neil Lennon's visitors snatched a 3-2 victory over Pedro Caixinha's side.
Promoted Hibernian fell behind just two minutes in when Colombian striker Alfredo Morelos headed in a Daniel Candeias free-kick, but Simon Murray levelled for the visitors, and they were soon in the ascendancy once Rangers midfielder Ryan Jack was shown a straight red card by referee John Beaton following a melee.
James Tavernier's own goal before half-time nudged Hibernian ahead and midfielder Vykintas Slivka drove in a third for the away team in the 65th minute.
Tavernier reduced the deficit with a header but Hibs, managed by former Celtic boss Lennon, held firm for the victory.
Celtic's 1-0 win on Friday night over Partick Thistle gave last season's champions six points from six so far, and Hibernian joined them on that mark, with St Johnstone and Aberdeen also both maintaining 100 per cent records by winning on Saturday.
St Johnstone took advantage of Motherwell's capitulation at McDiarmid Park, where the visitors had three players sent off in a 4-1 defeat. Goalkeeper Trevor Carson, skipper Carl McHugh and Charles Dunne were dismissed in the second half.
Saints secured an early advantage from Steven MacLean, and a double from on-loan Rangers forward Michael O'Halloran could have been a hat-trick, but he missed a late penalty before Murray Davidson netted St Johnstone's fourth. Andy Rose netted for Motherwell.
Aberdeen came from behind to win 2-1 at Ross County, recovering from conceding a second-minute header from Craig Curran to come out on top with goals from Mark Reynolds and Shay Logan.
Hamilton scooped their first three points of the season, thumping Dundee 3-0 with goals from Darian MacKinnon, Steven Boyd and Dougie Imrie. Imrie converted an 85th-minute penalty to complete the scoring, seven minutes after Scott Allan missed from the spot at the other end.
Hearts also got off the mark, following up last week's defeat at Celtic with a 1-0 win at Kilmarnock that was secured by a sixth-minute goal from Isma Goncalves.
The match-winner, whose 20-yard strike was an impressive finish, was sent off midway through the second half after a tussle with Kilmarnock centre-back Kirk Broadfoot, who was also red-carded.