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.
Durban City have officially confirmed the departure of interim coach Pitso Dladla, ending a successful chapter that saw him guide the club to Nedbank Cup glory and secure a place in next season's MTN8.
Orlando Pirates have reportedly completed the signing of Leicesterford City midfielder Matome Mmolai.
Miguel Timm, Njabulo Ngcobo and Sifiso Ngobeni are all reportedly set to leave Cape Town City following the club's unsuccessful Betway Premiership promotion bid.
Former TS Galaxy head coach has admitted negotiations with some Premier Soccer League clubs but denied any agreement following links with Golden Arrows.
