Albion goalkeeper David Stockdale made a crucial point-blank save to deny Tom Ince in the early stages before Darren Bent glanced a header wide.
Tomer Hemed tested Rams keeper Scott Carson with a half-volley after the break and the Israeli then had a goal-bound shot cleared by Cyrus Christie.
Stockdale palmed away a low strike from Will Hughes late on to secure a point.
Derby threatened in the early stages but Brighton managed to soak up the pressure and eventually created the better openings in what was a tight encounter.
On-loan Seagulls striker Glenn Murray had a shot blocked just before half-time and then headed over the bar in the second half.
Both sides finished in the top six in the Championship last season before being beaten in the play-off semi-finals, and are expected to challenge for promotion again.
Pearson, back in management following his sacking by Leicester in June 2015, won the Championship title with the Foxes in 2013-14.
Derby County boss Nigel Pearson:
"I was very pleased with our determination and the fact that the players kept on trying to function as a team. Although we weren't playing at our best and didn't use the ball as well as I would have liked to have done, we worked really hard to protect our own goal.
"We had some very good chances early on, we started the first half very well and they started the second half very well.
"What's important for me with this performance and this result is that if people have the opinion that in the past we may have lost, I was interested and very pleased to see our players work so hard to not allow a tight game to go to the opponents.
"You've got to try and win games but if you can't win them you don't lose them and I think both managers would be saying very similar things."
Brighton & Hove Albion manager Chris Hughton:
"I think in the last few years a draw here is going to be a very good result. I thought although we needed David Stockdale to make a couple of very good saves, we edged the chances.
"I thought we had the better of the chances but I thought on the balance of play a draw was probably a fair result. I think what you have with Glenn [Murray] is a player who will be a wonderful signing for us but he's come in on the back of a season last year when he didn't have too many starts.
"But he's a worker for the team so my delight with him is how he's got into those positions and if he does that enough times over a season he will score goals.
"Generally you don't know what you are going to get first game of the season but I thought the application of the team was excellent and apart from winning and goals I think I've got everything I wanted today."
Match ends, Derby County 0, Brighton and Hove Albion 0.
Second Half ends, Derby County 0, Brighton and Hove Albion 0.
Attempt saved. Darren Bent (Derby County) header from the centre of the box is saved in the bottom left corner. Assisted by Cyrus Christie with a cross.
Jacob Butterfield (Derby County) wins a free kick in the defensive half.
Foul by Beram Kayal (Brighton and Hove Albion).
Foul by Jacob Butterfield (Derby County).
Jamie Murphy (Brighton and Hove Albion) wins a free kick in the attacking half.
Substitution, Brighton and Hove Albion. Kazenga Lua Lua replaces Anthony Knockaert.
Attempt missed. Jacob Butterfield (Derby County) left footed shot from outside the box is just a bit too high.
Offside, Derby County. Will Hughes tries a through ball, but Darren Bent is caught offside.
Attempt missed. Will Hughes (Derby County) left footed shot from outside the box is close, but misses to the right. Assisted by Jeff Hendrick.
Attempt missed. Glenn Murray (Brighton and Hove Albion) header from the centre of the box misses to the right. Assisted by Anthony Knockaert following a set piece situation.
Foul by Will Hughes (Derby County).
Liam Rosenior (Brighton and Hove Albion) wins a free kick on the right wing.
Substitution, Brighton and Hove Albion. Jamie Murphy replaces Jiri Skalak.
Attempt missed. Jacob Butterfield (Derby County) left footed shot from outside the box is just a bit too high. Assisted by Chris Baird.
Attempt saved. Glenn Murray (Brighton and Hove Albion) header from the centre of the box is saved in the bottom right corner. Assisted by Jiri Skalak with a cross.
Jeff Hendrick (Derby County) is shown the yellow card for a bad foul.
Foul by Jeff Hendrick (Derby County).
Jiri Skalak (Brighton and Hove Albion) wins a free kick in the defensive half.
Substitution, Derby County. Jacob Butterfield replaces Tom Ince.
Chris Martin (Derby County) wins a free kick on the right wing.
Foul by Jiri Skalak (Brighton and Hove Albion).
Attempt missed. Anthony Knockaert (Brighton and Hove Albion) left footed shot from outside the box is close, but misses to the left. Assisted by Beram Kayal.
Craig Bryson (Derby County) wins a free kick in the defensive half.
Foul by Jiri Skalak (Brighton and Hove Albion).
Foul by Jeff Hendrick (Derby County).
Anthony Knockaert (Brighton and Hove Albion) wins a free kick on the right wing.
Richard Keogh (Derby County) wins a free kick in the defensive half.
Foul by Anthony Knockaert (Brighton and Hove Albion).
Substitution, Brighton and Hove Albion. Sam Baldock replaces Tomer Hemed.
Anthony Knockaert (Brighton and Hove Albion) is shown the yellow card for a bad foul.
Will Hughes (Derby County) wins a free kick in the defensive half.
Foul by Anthony Knockaert (Brighton and Hove Albion).
Corner,  Brighton and Hove Albion. Conceded by Jason Shackell.
Attempt blocked. Glenn Murray (Brighton and Hove Albion) left footed shot from the centre of the box is blocked. Assisted by Steve Sidwell.
Attempt blocked. Tomer Hemed (Brighton and Hove Albion) right footed shot from the right side of the box is blocked. Assisted by Glenn Murray.
Substitution, Derby County. Chris Martin replaces Nick Blackman.
Offside, Derby County. Tom Ince tries a through ball, but Darren Bent is caught offside.
Delay over. They are ready to continue.
Nigel Pearson saw his first game in charge of Derby end in a goalless draw against Brighton at the iPro Stadium.