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.
Golden Arrows and Stellenbosch FC played out a 1-1 draw at King Goodwill Zwelithini Stadium in Durban on Wednesday, in a Betway Premiership match that had crucial implications for the battle for a top-eight finish.
Mamelodi Sundowns coach Miguel Cardoso has warned his side against getting too comfortable at the top of the Betway Premiership standings.
Chippa United coach Vusumuzi Vilakazi admits his players need to improve their mental strength if they are to survive relegation from the Betway Premiership this season.
Mamelodi Sundowns moved two points clear at the top of the Betway Premiership standings after beating Marumo Gallants 3-1 at Loftus on Tuesday.
