Robinson latched onto Steve Morison's flick-on and applied a cool finish to leave the Eagles without a win in five matches.
Owen Garvan's free-kick caused problems in the box early on, Julian Bennett just failing to connect with his inviting ball into the box.
Bennett then fell to the floor after a group of players came together inside the box but referee Mick Russell was not interested in those half-hearted penalty claims.
Palace enjoyed some excellent pressure during the early stages, but Millwall had chances too, Morison's tamely hit shot from the edge of the area bobbling into the arms of Palace goalkeeper Julian Speroni.
Garvan's cross to the far post in the eighth minute looked promising but Andy Dorman failed to connect as it dropped out of the sky.
Morison had another chance for the visitors in the 13th minute, but from a tight angle, with the Lions striker opting for power, Speroni got down well at his near post to deny him.
A good Palace break at pace afforded Wilfried Zaha the chance to break but he failed to test Millwall goalkeeper David Forde, instead firing high and wide.
Robinson fizzed a shot just wide of Speroni's goal, while Chris Hackett's toe-poked effort on the half-hour mark, which was never on target, rolled just wide of the right-hand upright with Millwall on the offensive.
Patrick McCarthy spurned a glorious opportunity with half time fast approaching, blazing high over Forde's goal from just six yards, while Zaha also went close.
Millwall took the lead in the 53rd courtesy of Robinson's neat finish and second league goal of the season.
Morison outmuscled Bennett and nodded the ball on with his head for the fast-moving Robinson, who rounded Speroni with ease and slid the ball, which perhaps shaved the post on its way, into an empty net.
Zaha had more penalty claims waved away before, Morison brought a fine save out of Speroni as he ghosted into the box once more.
Robinson towered above Patrick McCarthy in the 63rd minute and powered his header down but it fell wide of the post on this occasion.
Zaha went clear shortly after but he was caught in two minds and the chance got away as several Lions defenders came swarming back.
Palace had another great opportunity with Forde doing brilliantly to deny Pablo Counago and then Zaha on the follow-up as the home side piled on the pressure during the closing stages.
The final chance of the match fell to Counago, but he could only find the side-netting after wriggling his way into the box.
Claude Davis was also sent off for an alleged stamp with seconds left to play.