West Bromwich Albion returned to the Championship in disappointing fashion, but there was better news for another side relegated from last season's Premier League, Swansea.
Meanwhile, preseason promotion favourites Nottingham Forest and Middlesbrough both made faltering starts to their campaigns.
West Brom went down 2-1 at home to Bolton Wanderers, for whom Yanic Wildschut scored an 89th-minute winner.
Swansea fell behind at Sheffield United, but second-half goals from Oliver McBurnie and 19-year-old Yan Dhanda turned the game in favour of the Welsh club.
Forest, who have spent heavily in the offseason, drew 1-1 at Bristol City with Daryl Murphy equalising just after half-time.
Middlesbrough, beaten in the playoffs last season, looked set for defeat at Millwall but scored twice late on to draw 2-2. Martin Braithwaite halved the deficit in the 87th minute and George Friend struck an equaliser in the seventh minute of stoppage time to spark wild celebrations from the away fans.
Brentford were the day's big winners, thumping promoted Rotherham 5-1; Neal Maupay scored twice.
Michael Jacobs bagged a brace as another promoted club, Wigan, celebrated their return to the second tier with a 3-2 victory over Sheffield Wednesday.
Blackburn also came up from League One and looked set to start with victory at Ipswich, only for substitute Tayo Edun to salvage a 2-2 drawn the 91st minute.
There was also late drama at Birmingham, where Viv Solomon-Otabor game the homreside a 2-1 lead in the 89th minute, only for Onel Hernandez to draw Norwich level in the fourth added minute.
Former England manager Steve McClaren's Queen's Park Rangers lost 1-0 at Preston North End.