Both teams showed intent from the off, with Samuel Chukwueze seeing a header palmed away before Tijjani Noslin’s first-time effort was denied.
Lazio made the breakthrough in the 10th minute, when Matteo Cancellieri nipped in at the back post to turn home Mattia Zaccagni’s low ball.
Either side of the cooling break, Mike Maignan did brilliantly to bravely rush out and stop Zaccagni’s attempt, then looked on gratefully as Davide Frattesi’s effort trickled agonisingly past the post.
Chukwueze tried to make things happen for Milan, and his pinpoint cross was headed over the crossbar by Strahinja Pavlovic, who could only watch on as Lazio doubled their lead in a bizarre fashion moments later.
Pervis Estupinan initially turned Kenneth Taylor’s low cross onto his own crossbar, before Noslin managed to head the ball in while Koni De Winter tried to clear.
There was still a scare as the break approached, with Ruben Loftus-Cheek’s strike deflecting off Zaccagni and fizzing wide before Mario Gila’s attempt from the ensuing corner was saved.
Ruben Amorim took action with a triple change ahead of the restart and his side came out on the front foot, threatening when Chukwueze’s shot was blocked by Oliver Provstgaard before delivering a cross that Pavlovic headed straight at Christos Mandas.
The goalkeeper then got a strong hand to Christian Pulisic's low drive, but there was nothing he could do when Moreira emphatically volleyed in fellow substitute Pulisic's looped cross in the 65th minute.
Outdoing himself mere moments later, Moreira met Adrien Rabiot’s lay-off and smashed the ball into the bottom corner to level.
Zaccagni saw an ambitious strike palmed away before Alphadjo Cisse curled his shot wide as both teams searched for a winner.
Moreira then got into the box again but hit the side netting, and an audacious Omari Hutchinson strike was held late on, forcing Milan to settle for back-to-back draws, which does at least keep them unbeaten this term.
Meanwhile, Lazio lose their perfect record but remain top of Serie A for now.
Flashscore Man of the Match: Diego Moreira (AC Milan)