The World Cup winner headed us ahead after 16 minutes, before doubling our lead six minutes later, combining with Kevin De Bruyne to slot into the bottom corner from a clever free-kick routine.
Rodrigo swept in an impressive third immediately after the interval, before the visitors netted a late consolation through Ameen Al-Dakhil.
Alvarez, who turned 24 today, now has eight goals in the league this season.
“It’s good goals isn’t it, to celebrate? I’m so happy for him because his season has been great,” said Rodrigo.
“He’s now 24 but he’s the future of this club. He’s so well adapted and I’m so happy for him.
“It was a tough game, it’s always not easy against these types of teams. They deserve credit.
“But we were focused from the first minute. I think you saw how difficult it was for them, we kept the ball and we played a complete game.
“In the second half with the third goal, we were a bit more relaxed. But it was a perfect game.”
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Rodrigo now has nine goal contributions in the top-flight this season, scoring five times and registering four assists.
The Spaniard declared his desire to continue helping the team in an attacking sense and is looking ahead to competing for trophies over the next few months.
“I was shouting at Phil [Foden] from halfway to pass it to me. I knew I was alone because everyone was dropping. It was a good touch so I’m very happy for that.
“I always say, I could improve in these situations, score more goals and be influential in the final third with assists. That’s my aim now, to grow in that part of the pitch. I’m doing good but of course I want more.
“We need to keep it in the same way. We’re doing very good and now it seems everyone is coming back. Erling [Haaland] is good news, John [Stones] also.
“So it’s good news, we need all of us because the second half of the season is going to be so tough.
“But we know how City are in this situation. We’re going to go for everything as always.”
