Forest, who have spent heavily in the off-season, drew 1-1 at Bristol City with Daryl Murphy equalising just after halftime.
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.
West Bromwich Albion, back in the second tier after being relegated from the Premier League last season, made a poor start as they went down 2-1 at home to Bolton Wanderers.
Former England coach Steve McClaren's Queen's Park Rangers lost 1-0 at Preston North End.
Wigan Athletic celebrated their return to the second tier with a 3-2 victory over Sheffield Wednesday.
(Reporting by Martyn Herman; Editing by Clare Fallon)
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