Sam Allardyce admitted Albion rode their luck after his first home win as Baggies boss.
Albion took the lead when captain Kyle Bartley headed home an 11th minute corner.
Brighton were then awarded a dubious penalty four minutes later which Pascal Gross fired across the crossbar.
The visitors then had a bizarre free-kick disallowed after referee Lee Mason blew his whislte twice in a matter of seconds. He then awarded the goal before consulting VAR and awarded another free kick.
The drama wasn't over after the break when former England international Danny Welbeck blasted another penalty against the post as the Baggies held on for three valuable points.
"It was obviously a game with a number of talking points," Allardyce told the club's official website.
“Brighton had the two penalties and missed both of them, and they also had the goal from the free-kick ruled out.
“I didn’t think the first one was a penalty. Okay hasn’t made an attempt to touch the ball with his hand. He’s jumping up to try and win the ball, not handle it.
“At least they didn’t score it. The second penalty, which I thought was a penalty, could then have been their winner if they had converted the first one.
“I think we’ve had a big slice of luck today. We’re glad to have a bit for a change.
“It’s clearly a big three points for us.It’s about time we won. We’ve had chances to win games against Fulham, Man United and Burnley in recent weeks.
“They were big points dropped, so to get these three points with a little bit of luck, I’ll gladly accept them.
“It doesn’t matter how we get them at this stage of the season. We just need to get them.
“If we were a bit fortunate or not, it doesn’t matter. We will wake up tomorrow with three more points on the board.”
What did you make of Albion's win over Brighton? Have your say at Baggies Banter.