Roma struck twice in the first half, Bryan Cristante firing in from the edge of the box before an Aleksander Kolarov free kick took a wicked deflection to beat goalkeeper Alessio Cragno.
Cagliari had Cragno to thank for keeping them in the game with two superb reflex saves on young midfielder Nicolo Zaniolo, before they mounted an extraordinary late rally.
Artur Ionita pulled one back with a header from a corner after 85 minutes before Cagliari coach Rolando Maran was sent off for dissent and two of his players, Luca Ceppitelli and Darijo Srna, were also shown red cards in stoppage time for the same offence.
Cagliari substitute Sau latched on to a defence-splitting through ball before finishing coolly to earn his side a draw with the last attack of the game.
Roma coach Eusebio di Francesco is facing increasing pressure after leading his side to one win in their last seven league games, and the draw in Sardinia means they remain outside the top six in seventh place on 21 points.
Cagliari are without a win in their last five Serie A matches but remain one of three teams to have avoided a home defeat this season, along with Juventus and Napoli, and the islanders occupy 13th place with 17 points. (Reporting by Alasdair Mackenzie, editing by Ed Osmond)
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