The Serie A outfit made the stronger start and took the lead with the first real chance of the game after 12 minutes.
Antonio Candreva unleashed a bouncing shot from distance and Palace goalkeeper Julian Speroni failed to gather, allowing Miroslav Klose to score from close range.
Palace new boy Jerome Thomas then limped off before Dean Moxey managed to bundle a Senad Lulic shot off the line.
And Speroni did well to deny Lazio a second goal soon after the interval, saving well from Lucas Biglia after the ball had rebounded into the midfielder's path.
Palace had struggled to create chances in the opening period but they were improved for the half-time introduction of new boy Dwight Gayle, who shot just wide approaching the hour mark after exchanging passes with Kevin Phillips.
The duo were soon combining again and Phillips drew a save from Federico Marchetti, who then blocked a goal-bound Gayle shot.
But Lazio ended up holding out for the win and they almost doubled the margin of victory late on, only for Ederson's header to fly just wide.