The hosts raced ahead courtesy of Matty Cash's long-range drive, but they did not lead for long.
Kyle Edwards brought the Baggies level a quarter of an hour in at the City Ground, and then fellow winger Matt Phillips' attempted cross went in - and was enough to give the visitors the three points.
On a day filled with debutants and goalkeeping gaffes, it was Albion who were the ones left smiling.
They did not undo Forest with attractive football, but they displayed encouraging grit - a quality very much needed to succeed in the second tier.
Yes, Aro Muric's dodgy display between the sticks for the home side - letting Edwards' strike through him, and Phillips' attempted cross over him - proved a big factor in starting the season soundly.
But the Baggies' organisation after they had managed to come from behind was impressive.
Semi Ajayi was an imposing presence in defence, heading anything that came his way clear.
Romaine Sawyers, although operating a little deeper than some may have expected, had a calming influence in midfield, where Filip Krovinovic also displayed flashes of his ability.
Kenneth Zohore, while he did not have a great deal of service to work with, put himself about up front, and youngster Nathan Ferguson did himself proud on his first-team debut.
He was tasked with marking Joe Lolley and Albert Adomah - two tricky customers who kept switching sides - and was rarely troubled by the dynamic duo.
Sam Johnstone should have kept out Cash's opener, but that was one of only a few negatives for Albion to work on. They frustrated Forest and were deserved winners.
Albion handed debuts to five players - new signings Zohore, Krovinovic, Ajayi and Sawyers, and teenager Ferguson. Another fresh face, Darnell Furlong, was among the substitutes.
Oliver Burke was also on the bench against his old club, while Sam Field did not make the squad despite being fully fit. Chris Brunt and Hal Robson-Kanu missed out through suspensions carrying over from last season.
With such a new-look side, it was fair to expect the Baggies not to make the sharpest of starts to the clash.
And it was Forest who began with more intensity, amid a cracking atmosphere at the City Ground - Kyle Bartley, in particular, targeted as the home side pressed high up the pitch.
They got their just deserts after a mere seven minutes, too. Cash played a swift one-two with Adomah before finding the bottom corner from 20 yards.
And while there was an element of surprise with the right-back's strike, Johnstone should not have been beaten at his near post.
But Albion, credit to their character, soon came up with a leveller. Edwards grabbed the spotlight as he waltzed into the area, worked the ball onto his left foot and guided it home.
It was a great solo effort, but, again, with definite question marks over the goalkeeping - Muric letting the low shot sail through his hands.
The theme of poor shot-stopping continued as well, and to the Baggies' benefit as they went ahead.
Phillips delivered the ball into the box from the right, looking for Zohore at the far post. He did not find the Danish striker, but the net rippled as the ball sailed over Muric, who made another mistake as he misjudged the flight of it.
So, there were promising signs in the first half for Bilic, seeing his men grit their teeth and turn things around after an early setback.
And it could have got better shortly after the restart as Forest were caught napping and Krovinovic broke up the pitch. Edwards was waiting to be released through on goal and potentially score his second. The Croatian took too long, though, and the pass was intercepted.
The game went into a lull for the next 10 minutes or so as the towering Ajayi marshalled the Albion backline.
It sprung back into action with a chance for the Baggies to extend their advantage. Gibbs galloped up from left-back before playing in Edwards with a perfectly-weighted through-ball.
And from a similar angle to which he scored at the other end, Edwards again pulled the trigger. This time, though, Muric stood tall and made a smart save.
Bilic's charges were very much on the lookout for another goal and freshened things up in attack as Burke replaced Zohore just after the hour mark. Burke - a Forest youth product - received a mixture of cheers and boos as he entered the fray.
Another substitution was soon made, and it was an enforced one as Gibbs limped off. Conor Townsend replaced him.
There was the odd scare for Albion. Alfa Semedo drove through the middle and unleashed a right-footed rasper which sailed just high and wide, while substitute Rafa Mir could not get on the end of a Lewis Grabban cross.
The Baggies, who also introduced Rekeem Harper late on, held on with relative ease in the end, though. A top evening's work.
7 - Goal! A poor start from Albion. Cash plays a one-two with Adomah before beating Johnstone at his near post from 20 yards. Surely the keeper's got to be saving that?
15 - GOOOOOAL! A swift response from the Baggies, and it is Edwards with a fine solo effort, working space and firing the ball low past Muric, who lets the strike fly through his hands.
26 - GOOOOALLLL!! Bilic's side are now in front! Muric is having a bit of a shocker for Forest. Phillips looks for the far post with his cross, but it ends up in the net as Muric misjudges the flight of the ball.
Forest (4-2-3-1): Muric; Cash, Worrall, Dawson (c), Robinson; Semedo (Johnson, 88), Watson; Lolley (Ameobi, 72), Silva (Mir, 62), Adomah; Grabban
Subs not used: Smith (gk), Ribiero, Figueiredo, Richardson
Goals: (Cash, 7)
Albion (4-3-3): Johnstone; Ferguson, Bartley, Ajayi, Gibbs (Townsend, 71); Livermore (c), Sawyers, Krovinovic; Phillips, Zohore (Burke, 63), Edwards (Harper, 84)
Subs not used: Bond (gk), Furlong, Leko, O'Shea
Goals: Edwards (15), Phillips (26)
Referee: Darren England (South Yorkshire)
Attendance: 27,592, (1,991 Albion)