Boro went into the match without a victory in nine Premier League matches, while West Brom, bottom of the table going into the match, had only won five league matches all season.
But both teams served up a match full of excitement, and quality attacking play.
Gareth Southgate's Middlesbrough side created several fine chances but were made to pay for some sloppy finishing.
And the manner of the Baggies' opening goal will no doubt have infuriated the visitors just as much as their wastefulness in front of goal.
The scorer Brunt seemed to be about three yards offside from the initial pass.
But Tony McMahon's weak defensive header fell to Brunt and the winger's 12-yard left-foot strike took a cruel deflection off McMahon and into the far corner of Ross Turnbull's net.
Boro and indeed those who pen the "Laws of the Game" will argue Brunt was not offside in the second phase of play but neither manager will be certain a similar goal would be allowed to stand next time out.
But while the legitimacy of West Brom's strike was still being discussed by a furious Southgate and his Boro bench, his players very nearly drew level.
Boro have work to do - Southgate
Within seconds of the restart Alves saw his header crash back off the bar and to safety.
The Brazilian had two more excellent first-half chances, but shot wide after David Wheater flicked on Andrew Taylor's long free-kick and then saw his shot blocked by Scott Carson after a neat run and turn.
Both sides were looking lively going forward but much of that could easily be put down to the fact both were also looking shaky at the back.
Jay Simpson had a wonderful chance to add a second home goal but was denied a superb piece of goalkeeping by Turnbull who dived at the on-loan Arsenal striker's feet as he raced through one-on-one.
Brunt then headed wide from Carl Hoefkens' cross after more excellent work by Simpson.
Both sides were forced into a defensive reshuffle in the latter stages of the first half, with Boro's Chris Riggott and West Brom's Leon Barnett coming off.
The changes did little to tighten things up and the pulsating pace continued after the break.
Alves saw an effort go wide for the visitors and Simpson was denied at the other end by a fine Turnbull save.
Mowbray pleased to generate chances
But any hopes of Boro earning something from the game disappeared in the space of 13 second-half minutes.
Another deflected strike saw Albion double their lead when Koren ran in from the right-flank, exchanged passes with Fortune and then saw his clever effort beat the unlucky Turnbull via a huge deflection off Fortune.
Seconds later Boro's afternoon got even worse when Digard was dismissed for appearing to jump into a challenge on Valero.
West Brom had chances to increase their margin of victory in the closing stages but had to settle for a 3-0 win against an increasingly shambolic-looking Boro.
West Brom manager Tony Mowbray:
"We are off the bottom but getting out of the bottom three is a more crucial psychological barrier to overcome and we are going to have win a few more games to make that happen.
"In Premier League games you have to win back-to-back games to get out of trouble. No-one at our club is thinking we have achieved anything.
"We have given ourselves a chance by bringing the rest of the league back towards us a little bit and we will enjoy the second half of the season.
"There are some fixtures we can look forward with, total respect to them, against the likes of Sunderland, Newcastle, Wigan and Bolton, the sort of teams who are in and around us.
"They have all still to come to the Hawthorns and they are games, if we are right on the day, we can win."
Middlesbrough boss Gareth Southgate:
"We have been beaten 3-0 at the bottom team and how we come through this is the important thing. We understand the spotlight will be on us. Everyone will be asking plenty of questions about us.
"We have to stand strong, we have to take the criticism, and we have to respond with what we do on the field. We have to stand firm as a group.
"Everyone has got to look at themselves first and then the overall picture of what needs to improve.
"We can't hide from the fact we've gone 10 league games without a win but these are some of the challenges you face in football and you have to get on with it.
"We have got to get a win. This was a good opportunity. We didn't play with a lack of confidence in the first half.
"But we weren't good enough in certain areas of the field and we have to rectify that. We didn't defend well enough and we didn't take our chances."
West Brom: Carson, Hoefkens, Barnett (Pele 39), Donk, Robinson, Borja Valero, Greening, Brunt, Koren, Simpson (Moore 77), Fortune (Beattie 69).
Subs Not Used: Kiely, Cech, Kim, Filipe Teixeira.
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