Bournemouth took a first-half lead through Emiliano Marcondes, before Dara O'Shea's header levelled things up before half-time.
Marcondes' fellow Dane Phillip Billing made things 2-1 just after the break, but Valerin Ismael's former Barnsley captain Alex Mowatt - who he bought with him to West Brom - crossed for Callum Robinson to score the equaliser.
Bournemouth's Scott Parker and West Brom's Ismael were both taking charge of their first games for their respective clubs, and they were both seemingly happy with a point.
The fans flooded back into the Vitality Stadium on Friday evening which, after months of empty stadiums, was a more than welcome sight.
The two goalscorers for Bournemouth were two of only a few players in the squad to not have graduated from the Cherries' academy - with 11 of Parker's 18-man group produced by the club.
Teenagers Jordan Zemura, Gavin Kilkenny, and Jaidon Anthony, who had only made a combined eight appearances for the club before tonight's game, all impressed under the lights.
Anthony got the assist for Marcondes' opener, with a superb cut-back to the new signing from Brentford.
Zefura also had a hand in a goal, as he crossed to Billing for his second-half strike, whilst also keeping West Brom's key man Grady Diangana quiet at the other end.
Kilkenny was the man that particularly impressed David Connolly, however, and the former Championship striker told talkSPORT that he was amazed by the Irishman's maturity in midfield.
Connolly said: "He took the ball down, span and played a lovely ball over the top. Incredible.
"He can break things up and he can play a pass.
"He's in there on his own at times because Parker plays two central midfield players, but it's only really him in there. Marcondes and Billing are more advanced midfielders."
West Brom responded to Bournemouth's opener through O'Shea header, as the Ireland international rose highest at the back post and headed past his countryman, Mark Travers.
Whilst neither of the Baggies goals came directly from a throw-in or corner, Ismael's side caused problem after problem from set-pieces throughout the game.
Last season, Ismael's Barnsley were known for their physicality, and his West Brom side looks to be no different this campaign.
Connolly was bemused as to why Bournemouth kept giving the Midlanders the opportunity to hurl a ball into the box, as they struggled to keep out the aerial threat of the Baggies.
"They're not messing around West Brom. They're happy to put the ball in the box, even from deep positions," said Connolly.
"Anyone who saw Barnsley under Ismael, they will know he was very direct. They're not messing around.
"You've got to stop giving throws away. Instinctively, you put it out for a throw-in but you need to do better. You need to remember it's West Brom.
"Rather than booting it into the stand, have some composure and do more with it."
"They are a force to be reckoned with when they go direct, West Brom."