Reds boss Jurgen 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.
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 Sonny Turner's player ratings
1. Robert Sanchez- 4
Nowhere near the ball when rushing to close down Diaz for the opening goal, and was extremely fortunate not be sent off having smashed straight into the Liverpool forward. Distribution was poor throughout.
2. Tariq Lamptey- 5
An otherwise good display was marred by a moment’s loss of concentration in which he let Diaz speed away from him without following, the Liverpool forward subsequently heading in the visitor’s opener.
3. Lewis Dunk- 6
Didn’t do a lot wrong in conceding both goals, and defended well in the air. Always willing to put his body on the line to block shots, the Brighton captain had a competent game.
4. Joel Veltman- 5
Another player who failed to make a mark on the game. Had his pocket picked by Sadio Mane in a dangerous area which lead to a good chance for Liverpool, from which Mane should have done better.