The Baggies stormed ahead in a frantic first half thanks to Cedric Kipre’s 22nd-minute strike and John Swift’s 27th-minute thunderbolt, but Boro replied a minute later through Emmanuel Latte Lath.
Albion struck quickly in the second period through Brandon Thomas-Asante to make it 3-1 before Tommy Smith was shown his marching orders for the visitors soon after.
Marcus Forss did convert a late penalty, but the Baggies made sure of the points when Jeremy Sarmiento struck in stoppage time.
The first notable opportunity fell to the visitors, but it was of West Brom’s own making. Semi Ajayi, when receiving Okay Yokuslu’s pass inside his own penalty area, was caught in possession by Riley McGree and the Australian poked a low effort at goal which Alex Palmer was able to save with his leg.
Passing up that chance would prove costly, as Albion went up the other end and produced the afternoon’s first goal.
Darnell Furlong’s long throw-in was contested by Ajayi and Darragh Lenihan, but the loose ball fell to Kipre, who made room for himself, chested the ball down and struck a smart half-volley past Seny Dieng.
West Brom doubled their advantage a little over five minutes later when Jayson Molumby fed Swift, who was allowed time and space to drive forwards from midfield and fire a powerful shot into the top corner.
The first half fun and games were not done there, though, as Boro hit back instantly. Samuel Silvera ran at Matt Phillips on the right-hand side and the cross which followed was nodded past Palmer by Latte Lath.
The Ivorian centre-forward might have doubled his own tally before half-time, but he lifted another attempt over Palmer and also over the bar.
Equally, Albion could have extended their advantage at the other end, but Phillips pulled a low shot just wide of the far post.
Boro right-back Smith was booked for catching Jed Wallace just before half-time but it was his full-back counterpart Lukas Engel who endured a nightmare beginning to the second period when his attempted pass back was cut out by the lurking Thomas-Asante, who nipped in, took advantage of the loose ball and rounded Dieng before calmly rolling the ball home.
The Baggies were two goals to the good again, and shortly after they had a man advantage too, when Smith pulled Phillips’ shirt on the run and was dismissed with his second booking.
The home side, though, failed to put the game to bed and 10-man Boro were encouraged in the later stages when Isaiah Jones’ cross from the left struck the arm of Furlong and fellow substitute Forss rolled home the resulting penalty.
But West Brom would prevail when on-loan Brighton forward Sarmiento collected the ball from former Boro loanee Alex Mowatt in the penalty area before rifling his shot into the roof of the net.