The hosts showed two changes to the team that started the 2-0 victory over Bournemouth, with Adam Webster and Steven Alzate replacing Shane Duffy and Jahanbakhsh.
Blues head coach Frank Lampard recalled Jorginho, Reece James and Christian Pulisic in place of Mateo Kovacic, Fikayo Tomori and Emerson, as he made three alterations to the side that won 2-1 at Arsenal.
The visitors enjoyed the better of the early possession before the recalled Alzate saw a deflected effort fly inches wide of target at the other end.
However, it was the Blues who broke the deadlock with ten minutes played as Cesar Azpilicueta pounced on the loose ball after a Tammy Abraham shot had been blocked on the goal-line by Aaron Mooy.
Albion were then forced to replace defender Dan Burn following a clash with James, with Bernardo taking his place, as the visitors continued to control much of the possession.
The home side eventually carved out an opening when Leandro Trossard forced a save from Kepa Arrizabalaga, having been set up by the busy Neal Maupay.
At the interval Albion replaced midfielder Yves Bissouma with striker Aaron Connolly, but the hosts continued to find it hard trying to disrupt the assured play of the visitors, who saw Christian Pulisic drive a shot straight at Mat Ryan.
Pulisic was then replaced by Callum Hudson-Odoi, before Kepa made a fine save to keep out a sharp effort from the lively Connolly.
However, he was unable to do anything about a fantastic, acrobatic overhead effort from substitute Jahanbakhsh six minutes from time, with the Iranian scoring his second goal in two games in superb style.
Maupay then had a great chance to snatch all three points but Kepa made a fantastic save to deny the former Brentford ace from close range to secure at least a share of the spoils for the Champions League chasers.