Pizzi's side appeared to be labouring to a goalless draw after an encouraging start fizzled out into stalemate in their Confederations Cup opener in Moscow.
But Alexis, not fit enough to start due to an ankle injury, came on after 58 minutes and, despite not looking fully fit, created goals for Arturo Vidal and Eduardo Vargas as Chile got their Group B campaign off to a winning start.
Asked about the Arsenal man, Pizzi said: "He played a key role in both situations that led to a goal, so he's happy.
"I don't like mentioning individual players but we can be very happy that he plays in our national team. He always wants to play with us so we have to take care of him, even if that means he can't always be here when we want him."
It was Alexis's cross that Vidal nodded home to put Chile 1-0 up with 10 minutes to go and he also played a pivotal role in the second, dribbling round Cameroon goalkeeper Fabrice Ondoa to enable Vargas to fire home.
"All the players on the bench can join the game at any time," added Pizzi.
"In this situation, when you have an excellent player of course you try to find a time when he can come on and we wanted to see that. He has had some health issues but he played well and didn't suffer any more problems.
"The match really required us to do something to score a goal and he's the right player for that. He's a very important player and that's why we put him on."