The Argentine ace initially miscontrolled a high Liverpool ball.
But as he tried to recover his position, the centre-back could only clumsily clatter into Egyptian international Salah.
Otamendi was given a yellow card for his efforts.
The 29-year-old was drafted in from Valenica in 2015. He's played 63 games for the club and scored two goals.
City are 2-0 up at half-time following goals from Sergio Aguero and Jesus.
Sadio Mane has been dismissed for Liverpool following a high challenge on goalkeeper Ederson.
Liverpool have scored in 13 successive games against City in all competitions.
But City are currently on an 11-game unbeaten run - and Sergio Aguero has scored in all five of his Premier League appearances against Liverpool at the Etihad.
Man City: Ederson, Walker, Stones, Otamendi, Mendy, Danilo, Fernandinho, De Bruyne, Silva, Aguero, Jesus
Subs: Bravo, Foden, Mangala, Sane, Gundogan, Delph, Bernardo
Liverpool: Mignolet, Alexander-Arnold, Matip, Klavan, Moreno, Henderson, Can, Wijnaldum, Salah, Mane, Firmino
Subs: Karius, Lovren, Gomez, Milner, Oxlade-Chamberlain, Solanke, Sturridge