Bucs found themselves a goal down to a 22nd minute Andile Jali strike at the Orlando Stadium on Wednesday evening before Tshegofatso Mabasa levelled from the penalty spot four minutes into injury time at the end of the first half.
Monnapule Saleng then popped up with a winner in second-half stoppage time for a 2-1 win.
Reflecting on the result, the Pirates mentor told SuperSport: "Important points, good start with a victory. One year we started with zero and today we start with three.
"Chippa is a complicated team because they are big boys, very physical, it's difficult to contain them. But we managed to come back in the second half. I think we played good football in some moments."
Riveiro added though that Pirates must make sure they start better in upcoming games after conceding first in this game.
"We created more than enough chances, but in a rush," he explained.
“And coming from behind is not a good thing. It's not a habit that we want to create. We want to start games better and be ourselves, getting the advantage and not like today.”
Pirates are next in action against Jwaneng Galaxy in the second leg of their second preliminary round CAF Champions League qualifier on Saturday, where they hold a 2-0 advantage.
Orlando Pirates attacker Relebohile Mofokeng said it was important to return to winning ways after scooping the Man of the Match award for his performance and goal in the 2-0 Betway Premiership win over Magesi on Saturday.
Orlando Pirates coach Abdeslam Ouaddou was proud of his side's 2-0 victory over a struggling Magesi side but admits they should have netted more goals.
Chippa United beat Durban City to improve their chances of avoiding relegation from the Betway Premiership, while AmaZulu kept their momentum going.
Orlando Pirates returned to winning ways and reclaimed second place on the Betway Premiership table with a controlled 2-0 victory over Magesi FC on Saturday evening.
