Bacca scored before halftime on the break, while Niang converted from the spot late on after handball by Stefan Radu.
New coach Vincenzo Montella's Milan side are gaining momentum having lost twice this season and move up to third on nine points after seeing off Lazio, who are seventh on seven.
"The solid spirit we've had for the last two matches is what we need going forward," Milan captain Riccardo Montolivo told Mediaset Premium. "We did well to be clinical and efficient."
The unerring Bacca stroked the ball past stand-in debutant keeper Thomas Strakosha in the 37th minute after being released through the middle by Juraj Kucka, who quickly capitalised on Marco Parolo's poor control as a Lazio attack broke down.
"We should have taken the lead but instead we conceded a silly goal," said Lazio coach Simone Inzaghi. "We tried to recover the situation but weren't as organised after the break."
Milan could have doubled their lead before halftime when Lazio's backline was exposed by the fleet-footed Suso and the nervous Strakosha was forced to parry the ball clear after the Spaniard's cross was deflected goalwards by defender Bastos.
LAZIO CHANGES
Lazio made two changes at halftime and substitute Keita fired over early on after outmuscling two defenders.
However, the Rome side's wait for a first Serie A win against Milan at the San Siro since 1989 continues.
"We came here and made Milan play badly, they didn't have any fluid passing moves," Inzaghi added. "We played with character but still lost."
Milan extended their lead through Niang's 74th-minute penalty as the 21-year-old sent Strakosha the wrong way after his cross had been handled by Radu.
"(The match) against Fiorentina at the weekend will be a vital game for European qualification," Montolivo added, "which is an objective we're keen to achieve."
Champions Juventus, beaten 2-1 by Inter Milan on Sunday, host Cagliari in one of nine Serie A matches on Wednesday, while early leaders Napoli visit Genoa and Crotone travel to AS Roma.
(Reporting by Ed Dove; Editing by Toby Davis and Ken Ferris)
