An afternoon which started so brightly for Rotherham United ultimately ended in disappointment on Championship opening day.
The Millers led 2-0 after 20 minutes of new manager Alan Stubbs' first match in charge and were still in front at 2-1 when Wolves were reduced to 10 men early in the second half.
But a 65th-minute equaliser from Icelandic Euro 2016 hero Jon Dadi Bodvarsson changed the celebratory mood in the sunshine at a packed AESSEAL New York Stadium.
The home side will be encouraged by a terrific first half-hour, with new signings Will Vaulks and Jon Taylor to the fore, but still have work to do to tighten up defensively.
Rotherham swept into a ninth-minute lead when winger Forde took a corner from the right and striker Danny Ward's well-placed header went beyond Wolves goalkeeper Carl Ikeme.
New York was rocking nine minutes later when midfield man Vaulks marked his debut with a stunning 25-yard volley which thundered into the net to put the Millers 2-0 ahead.
But the visitors reduced the deficit in the 39th minute as George Saville rounded keeper Lee Camp to put the ball into an empty net for a goal the away side didn't really deserve.
Wolves were down a man after 52 minutes when Dominic Iorfa saw red for pulling back Taylor when the winger was scampering through on goal, but they equalised in the 65th minute as Bodvarsson latched on to substitute Joao Teixeira's pass to finish with precision into the top far corner.
Six minutes before Bodvarsson's strike, Ward had failed to make it 3-1, just unable to connect right in front of goal with a great Vaulks ball in.
Stubbs handed debuts to four new boys - Vaulks, Forde, Taylor and Jake Forster-Caskey - and there was no place in the starting 11 for Richie Smallwood or Greg Halford, two stars of last season's survival mission.
The Millers looked good at times in possession, but will be frustrated they couldn't dominate in the second half when they had the numerical advantage.
Goals: Ward 9, Vaulks 20 (Rotherham); Saville 39, Bodvarsson 65 (Wolves).
Rotherham United ( 4-3-3): Camp; Kelly, Broadfoot, Wood, Mattock (Thorpe 71); Frecklington (Smallwood 67), Vaulks, Forster-Caskey (Allan 76); Forde, Ward, Taylor. Subs not used: Price, Halford, Wilson, Yates.
Wolves (4-3-3): Ikeme; Iorfa, Batth, Hause, Doherty; Edwards, Evans, Saville; Wallace (Mason H-T), Bodvarsson (Costa 88), Henry (Teixeira 63). Subs not used: Lonergan, Coady, Price, Deslandes.
Referee: Scott Duncan (Northumberland).
Attendance: 11,291 (2,567).