Craig Mackail-Smith, Albion's £3.25million record signing from Peterborough, struck the winner moments before half-time at Fratton Park to make it two Championship wins out of two for Gus Poyet's side.
Pompey should have grabbed a point but Lawrence hit the post with his spot-kick, and their miserable week, during which they were dumped out of the Carling Cup by Barnet, ended in derby-day defeat.
The hosts had received a huge boost before kick-off when former crowd favourite Benjani was paraded to the fans after rejoining on a free transfer from Blackburn this morning.
Their afternoon almost got even better inside the first minute when Kanu teed up David Norris, but the midfielder put his shot narrowly wide.
Home skipper Lawrence then almost punished a defensive mix-up from the Seagulls but Lewis Dunk managed to get a block in.
Brighton were dealt a blow after 24 minutes when dangerman Will Buckley, who scored both goals in their opening-day win over Doncaster, limped out of the action.
But they came close to grabbing the lead on the half-hour when Gary Dicker's free-kick found Romain Vincelot, whose shot forced a fine save from Jamie Ashdown.
And the Seagulls did break the deadlock in first-half stoppage-time when Ashdown blocked a shot from Ashley Barnes and Mackail-Smith was on hand to toe the ball over the line.
There was still time for Lawrence to force a save from Albion goalkeeper Casper Ankergren before the half-time whistle.
After the break, veteran Pompey full-back Hermann Hreidarsson charged forward, skipping past three Albion defenders, only for his shot to hit Barnes and go out for a corner.
Norris should have done better when he was teed up by Lawrence but put his effort too high.
At the other end Craig Noone's angled drive was arrowing into the net until Ashdown dived to his right to pull off a superb save.
Pompey came close to a leveller in the 80th minute when Lawrence fizzed the ball across goal and the stretching Dave Kitson was inches from getting the decisive touch.
Some dozy Albion defending then gifted Norris another opportunity with four minutes remaining, but the summer signing from Ipswich blazed his shot over the crossbar.
In the fifth minute of injury time, they were thrown a lifeline when Dunk handled in the area but Lawrence could not find the target from the spot.