Paredes has been largely kept out of the Chile team by Humberto Suazo, the side's top scorer, but with Suazo injured, he has a chance of starting Chile's opening Group H match against Honduras on June 16.
On this showing, in the two sides' final training match before the tournament starts on Friday, he would be more than an adequate replacement.
He had the ball in the back of the net within six minutes but his effort was ruled out for offside, and found the net again just before the hour but this time was penalised for hand ball.
After midfielder Gonzalo Fierro had put Chile ahead on 68 minutes, Paredes finally got his name on the scoresheet in the 72nd minute to seal a comfortable victory for the South Americans.
With both side sides employing an army of substitutes and with the match split into three segments of 30 minutes rather than two halves, neither team found much in the way of momentum.
The Chileans had the better of it but despite the trickery of Alexis Sanchez and Fabian Orellana in their forward line, they constantly fell victim to New Zealand's disciplined offside trap.
The All Whites, who arrive in South Africa after a tour of Europe that included an impressive 1-0 defeat of Serbia, created little in the way of goal-scoring chances and relied heavily on long balls punted into the box.
The match was played in front of around 7,000 fans in a modest stadium ringed by spectacular hills in the Kanyamazane, close to the city of Nelspruit in eastern South Africa.
Chile will take on Honduras in Nelspruit next week while New Zealand will return to the city later in the tournament for the toughest of their three group matches, against defending champions Italy.