Victory narrowed the gap on leaders Man City to just three three points, with Pep Guardiola's team next in action on Monday night at Crystal Palace.
Klopp had said before the game he expected a reaction after the Reds experienced only their third defeat of the season courtesy of Inter Milan in midweek, but they struggled to get going before Diaz headed Liverpool ahead in the 20th minute.
Diaz bravely headed the ball into the back of the net before being clattered by Robert Sanchez as he rushed out of his goal.
The medics were immediately waved on by referee Mike Dean, but a subsequent VAR review allowed the goalkeeper to controversially remain on the field.
Graham Potter brought on Adam Lallana at half-time to face his former club, but the Seagulls midfielder lasted only seven minutes before being substituted.
The 33-year-old had only just returned from injury but was soon forced onto the sidelines again in the 52nd minute.
Liverpool added their second from the penalty spot in the 60th minute.
Dean had pointed to the spot after Naby Keita’s half-volley struck Bissouma on the arm.
Mohamed Salah stepped up to take the penalty and fired it past Sanchez and into the back of the net.
Shortly after scoring his 20th goal of the season, Salah was substituted.
The forward had gone down following a knock and was replaced by Diogo Jota.
Liverpool captain Jordan Henderson reflected on a job well done to secure the 2-0 triumph, saying on BT Sport: “It’s always pleasing to come away from home and get the three points.
“Brighton are a good footballing side. I know they’ve lost their last few but always dangerous, good technical players.
“They’ve troubled us at times over the last couple of years so it was a real big game for us today and I felt as though we delivered. Professional performance, three points on the road and we’re delighted with that.”
Scroll down and click through to see Sam Morton's player ratings
1. Alisson: 7 -
Brilliant reaction save to prevent Danny Welbeck from getting Albion back into the game. One of the only saves he had to make all afternoon. Was the subject of a controversial moment in the second half, with claims that he left his box with the ball in his hands. Despite huge appeals, the decision went Liverpool's way.
2. Trent Alexander-Arnold - 7:
A threat as always going forward, with some great passing moves, but also won his defence duels. Just lacked that final ball in forward areas, which we have come to expect from him.
3. Virgil van Dijk: 8:
An integral part of the Liverpool defence. Makes headed clearances — and football for that matter — look easy. He didn't give Maupay a look in.
4. Joel Matip: 7 -
After Brighton's bright start, Matip created the opening goal with an inch perfect through-ball for Luis Diaz. A moment which changed the change and Liverpool were largely untroubled from then on.