Tomer Hemed added a third after the hour mark before James Morrison pulled one back for the away side late on, but the Baggies created little and were outclassed by the hosts for large portions in what was Brighton's first top-flight win in 34 years.
Brighton edge into it
Tony Pulis made two changes the side that drew 1-1 with Stoke City a fortnight ago, as Jonny Evans returned to replace Chris Brunt, with Grzegorz Krychowiak making his league debut in place of James Morrison in midfield.
The hosts were unchanged as Chris Hughton elected to name the same XI that took a point away from Vicarage Road last time out.
After a predictably cautious start from both sides, Brighton slowly began to find their feet.
The hosts thought they had taken the lead in the 14th minute when Solly March's swerving 25-yard effort was parried by Baggies stopper Ben Foster into the path of Brighton's Shane Duffy, only for the Seagulls centre-back to be ruled offside.
Brighton stung the palms of Foster on two more occasions after efforts from Anthony Knockaert and again from Dale Stephens, but the West Brom 'keeper remained unbeaten.
Despite creating little in the final third, the West Midland side were predictably menacing at set pieces. On one such occasion, a Matt Phillips corner was flicked on by Ahmed Hegazi, only for the Egyptian's header to narrowly evade a team-mate in the six-yard area.
With the half-time whistle approaching, then came the moment Brighton fans had been longing for.
Just second before the break, March's cross to the back post was mis-judged by Allan Nyom, with the ball dropping to Groß. The German's shot was on target, but then deflected off a Baggies defender past a helpless Foster.
Referee Michael Oliver blew his whistle for the break, with the AMEX jubilant.
Groß doubles hosts' lead
With the hosts buoyant following their opener, Groß then added a second to double their advantage.
He evaded the advances of the Baggies defence, to stretch out and shy from the edge of the box, as his shot squirmed past Foster to make it 2-0.
The visitors were out of sorts from the side that have taken seven points from nine so far this season. Pulis responded by hauling off Hegazi and Salomon Rondon off for debutant Kieran Gibbs and winger Oliver Burke shortly before the hour mark.
The changes made little or no difference and on 63 minutes, Brighton were seemingly out of sight.
Again the lively March was the creator, as the winger clipped a weighted ball for Hemed and the striker notched his first goal of the season with a cushioned header at the near post.
Morrison spares Baggies' blushes
In truth, West Brom deserved little for their efforts on the South Coast, but were rewarded for the endeavours of their substitutes.
A cross from the right found Burke in the penalty area, who nodded back smartly to the on-rushing Morrison. His shot skidded under the challenge of Lewis Dunk, with Brighton keeper Matt Ryan unable to prevent the ball crossing the line, giving Pulis' side a consolation.
That was all it was however, as the hosts eased to their first Premier League win, to the relief of Brighton fans and boss Hughton.