Sunderland midfielder Andy Reid found the target with a dipping 20 yard effort but it did not trouble West Brom goalkeeper Scott Carson.
A low centre from Albion's on-loan Arsenal striker Jay Simpson took a deflection and fell invitingly to Robert Koren 15 yards out but his left-footed shot was blocked by Teemu Tainio.
Sunderland responded and a quick break by Cisse found them with a three versus two advantage but Abdoulaye Meite rescued the situation with a solid tackle on the Black Cats leading scorer.
It was 26 minutes before Marton Fulop, who had replaced the injured Craig Gordon, was extended for the first time, holding onto a low left-footed shot from Brunt which took a slight deflection.
Carson could only palm a cross from Reid into the path of Edwards but he appeared to be taken by surprise and his header looped harmlessly over the bar.
Richardson brought a fine full-length save out of Carson with a swerving 30 yard drive which was turned around the post.
Then after 40 minutes central defender Olsson broke the deadlock by putting Albion in front with his third goal of the campaign.
Skipper Jonathan Greening's inswinging corner flicked off the head of Abdoulaye Meite to Olsson at the far the post and his low left-footed half volley flew past Fulop.
Mowbray made a double half-time substitution with Youssouf Mulumbu and Shelton Martis replacing Simpson and Meite respectively.
The Black Cats made their first change after 52 minutes with Reid making way for Dean Whitehead and shortly afterwards Steed Malbranque came on for for Edwards.
Fulop had to come racing out of his area to deny Brunt after he had attempted to run onto a fine pass from Koren in a rare moment of excitement.
But after 58 minutes Brunt scored his fourth goal in the last three games to double the Baggies lead.
Fortune showed his power to shrug off the challenge of Anton Ferdinand and his low cross from the by-line was turned home at close range by the former Sheffield Wednesday man.
The impressive Dorrans limped out of the action after 63 minutes as Juan Carlos Menseguez became the third Albion substitute.
Cisse then missed a golden chance to reduce the arrears when he deflected a shot from Tainio over the bar from close range.
With a minute left, Brunt turned creator as his pass was turned home by Menseguez.
