The win has made it seven points from three games - making the team's recent four-game winless run a distant memory.
Brunt told the WBA website: "We went off track a little bit with three successive defeats but now we're unbeaten in three and we've won our last two.
"It's very important in this league to pick up back-to-back wins.
"For 60 to 70 minutes, we were the better side. We created more chances and on another day Romelu may well have scored his two one-on-ones.
"Any Premier League side is going to cause you problems when they're trailing at home and they threw everything at us in the last 20 minutes.
"But we battled away, as we have done all season, and managed to hold on for the win.
"We showed that we're a good bunch of lads that work hard for each other week in, week out."