Story of the match
The opening chance of the game fell the way of the visitors, Alex Mowatt delivered a beautiful free-kick and found the head of Karlen Grant, however, his header was straight into the arms of Mark Travers.
Shortly after, Marcondes opened the scoring for the Cherries, Jaidon Anthony did well down the left, his cross found Marcondes who turned home beyond David Button in the Baggies goal.
The game went quiet after that goal with no real goal mouth action, until the 33rd minute, O'Shea managed to head home from close-range after a superb cross by Conor Townsend to bring the visitors level.
Valerien Ismael's side thought they had took the lead four minutes later, a corner came in and hit Robinson before going over the line but the referee blew for an apparent push on Travers, however, looking at the replay, the goal should have stood.
The Baggies went close again before the half-time interval as Robinson fired an effort from the edge of the area only for Travers to push it wide.
The first chance for the Cherries after the break produced a goal, which came against the run of play, despite the Baggies starting the better of the sides after the restart, a good move down the left involving Anthony and Jordan Zemura saw the left-back pull the ball back for Billing to fire home.
The visitors went close through Darnell Furlong, a free-kick from Mowatt found the head of Furlong whose header flied over the bar.
Three minutes later, we were all square again, Matt Phillips played a neat one-two with Mowatt whose cross found Robinson who turned home from close-range.
Bournemouth thought they were in the lead for a third time, a cross from the left found David Brooks whose decent effort was pushed away brilliantly by Button, before, Grant managed to get beyond Chris Mepham and fired his effort wide.
Button was called upon again with just 12 minutes remaining, Dominic Solanke raced onto a long ball over the top and drove an effort towards goal but the Baggies keeper made a smart stop.
That was the last meaningful action of the game and both the Cherries and the Baggies had to share the spoils.
Ismael should be delighted with the response
The Baggies didn't give up throughout the game and had a few chances to win it, Bournemouth had chances too but overall Ismael should be the happier of the two managers on the opening day.
AFC Bournemouth: Travers, Smith, Mepham, Kelly (C), Zemura, Marcondes, Kilkenny, Billing, Brooks (Saydee 90+2), Solanke, Anthony.
Substitutes (not used): Dennis, Taylor, Rossi, Glover, Moriah-Welsh, Camp.
West Bromwich Albion: Button, O'Shea, Bartley, Kipre, Furlong, Livermore (C), Mowatt, Townsend, Diangana (Phillips 64), Robinson, Grant (Zohore 87).
Substitutes (not used): Johnstone, Ajayi, Tulloch, Ingram.
Referee: Darren Bond
Assistants: Mark Russell and Daniel Leach
Fourth Official: Andy Woolmer