Lautaro Martinez kept up his fine start to the season to open the scoring in the 30th minute of Monday's (AEST) clash, lashing in a shot which Thomas Strakosha failed to keep out.
But with Romelu Lukaku wasting a chance to double Inter's lead, Sergej Milinkovic-Savic's brilliant header restored parity.
Lazio's hopes of a comeback were dented in the 69th minute as Immobile, who managed just one shot from 26 touches in a frustrating individual display, saw red for slapping Arturo Vidal.
Inter almost snatched the points in the closing stages when Marcelo Brozovic struck the woodwork, before Nerazzurri substitute Sensi received his marching orders for hitting Patric.
Having lost Stefan Radu to injury, Lazio had the first meaningful attempt in the 19th minute, with Samir Handanovic palming Luis Alberto's strike over.
Handanovic's goalkeeping counterpart Strakosha failed to cover himself in glory as Inter hit the front 11 minutes later – the Lazio man only able to parry Martinez's low effort into the net.
Ivan Perisic bundled the ball into Martinez for that goal, and the winger would have had his second assist had Achraf Hakimi put a header on target.
Lukaku was inches away from adding a second after the restart, with Martinez then firing just wide of the upright.
Yet Lazio soon hit back, as Milinkovic-Savic sent a towering header in at the back post after connecting with Francesco Acerbi's excellent cross.
Lazio looked good for a second but their efforts were derailed when Immobile reacted badly to a challenge by Vidal, who made the most of it. The referee sent Lazio's talisman straight off.
Brozovic saw a deflected effort clip off the post as Inter pressed to make their numerical advantage count, only for Sensi to receive a red card for violent conduct as both sides settled for a point.