With the score at 0-0, despite his side dominating the match, the Argentine coach brought on Haboush Saleh for Tony, the Ivorian forward, in the 63rd minute.
Nine minutes later, the substitute scored the only goal of the game after a weaving run to send Al Nasr out of the competition, in a game played at the neutral venue of Al Wahda's Al Nahyan Stadium on Saturday night.
"Tactics and substitutions sometimes work and sometimes don't work, but it did work for us tonight," said Calderon, who was overseeing his third game in charge of last year's league runners-up since taking over last month from Jorvan Vieira, the Brazilian who was appointed as Sharjah coach on Friday.
"Of course, Haboush scored the all-important goal but credit should go to the entire team. This was an important game to win because of the knockout format of the competition. It is never easy to win any game but full credit to my players."
Saleh dribbled through the Al Nasr defence and drilled a superb shot low across Abdullah Moosa Ali, the Nasr goalkeeper.
It was a victory that avenged their defeat to the Dubai club in the Pro League last weekend.
"I have had my share of scoring two or three memorable goals for the club, as well as for the UAE Olympic team, but this one was special and for my team," Saleh said. "We have had a poor season so far and I wish we can now look ahead more positively.
"It was also an important win because it keeps our hopes alive in the competition."
Al Nasr pushed for the equaliser and Mark Bresciano's free kick was brilliantly saved by Mohammed Al Ghuloom, the Baniyas goalkeeper, four minutes from time.
Walter Zenga, Nasr's Italian coach, said he was missing six players, including the injured Ivorian striker Amara Diane and the suspended Brazilian midfielder Leonardo Lima.
"At the end, one goal made all the difference," Zenga said. "It is hard to play the normal attacking game when you don't have the players. Under the circumstances, my team did pretty well.
"As I said earlier, the scheduling of the Cup games is not in the best interest of the teams. I am not being critical but we should go into a new competition fresh and without carrying any suspensions.
"The President's Cup should be played like how the King's Cup in Saudi Arabia is played. They play at the end of the season to give the top teams an incentive.
"I have been playing and been involved in the game since I was nine. I am 51 now. I am saying these out of my experience and not to criticise anyone."
Baniyas, playing a foreigner short after the departure of David Trezeguet, the former World Cup winner for France who was released at the player's request, wasted numerous opportunities to take the lead.
Amer Abdulrahman's dipping free kick crashed against the crossbar in the fourth minute.
From then on, Andre Senghor, the Senegalese striker, had the best of the chances, but his header was blocked by the outstretched foot of Moosa, who also recovered quickly to get up and stop Adnan Hussain's effort on the rebound.
Moosa did well to push out a close-range header from Senghor from a Yousuf Jaber cross just before the break. Then, five minutes into the second half, Senghor blasted over the crossbar from 12 yards when he was set up in front of the goal by Tony.