It was enough to seal the points and manager Mark McGhee was quick to note that in an instantly forgettable encounter: "The difference between the teams was one good cross."
Brighton arrived at the New Den on the back of a four-game losing streak that had coincided with the loss of influential striker Bobby Zamora.
The striker's knee ligament injury sustained in the home defeat to Norwich City has robbed the Seagulls of their most potent threat, and all the momentum gained from an opening day win at Burnley has all but disappeared.
The opposite can be said of the Lions, who have gone through a gradual healing process following their 6-0 mauling at the hands of Rotherham on the first Saturday.
But they are falling way short of the standards they set last season, and with striker Neil Harris still to break his goalscoring duck, Millwall are finding things tough as well.
Both sides' hesitancy in front of goal was evident in the first 45 minutes, punctuated by rare moments of excitement.
Andy Roberts brought a smart stop from visiting keeper Andy Petterson, while a long-range Paul Ifill effort cannoned from the keeper and Danny Cullip cleared.
Steve Claridge, a target for the travelling fans as a result of his Portsmouth connections, twice had the opportunity to break the deadlock.
And in the final minute of the half, Guy Butters headed a free kick against his own crossbar.
Things improved marginally after the restart, Claridge almost guiding a header over Petterson, while Ifill flashed a shot across goal.
Even after Ward had given the Lions the lead, there was little sign of Brighton as an attacking force.
The Seagulls failed to register a shot on target all afternoon and are clearly counting the days until Zamora's return.
Their frustration boiled over as Robbie Pethick's off the ball clash with Kinet saw him red carded with 15 minutes remaining