After making a mistake in Genoa's opener, Reina conceded a penalty but went on to stop Lasse Schone's spot kick in a dramatic match, which saw both teams finish with 10 men.
"I am quite cool during matches," Milan coach Marco Giampaolo said. "I wasn't really convinced it was a penalty, but Reina has so much character that I had faith in him, that he would redeem himself by saving the penalty."
Giampaolo was under pressure after his side had picked up just six points from the opening six rounds.
"The pressure was so high and we were drowning at the end of the first half," he added. "I asked the team to play the match of their lives, character-wise, and they gave their all."
Reina was a late replacement for regular Milan goalkeeper Gianluigi Donnarumma, who felt sick after the warmup. The veteran Spaniard was at fault for the opener as he misjudged Lasse Schone's 30-yard free kick, which gave Genoa the lead four minutes before the break.
Theo Hernandez leveled for Milan early in the second half and matters went from bad to worse for Genoa five minutes later, when defender Davide Biraschi was shown a straight red card for handball and Franck Kessie converted the resulting penalty.
However, Milan also had a player sent off when Davide Calabria was shown a second yellow card for a shirt tug on Genoa forward Christian Kouamé, 11 minutes from time.
Genoa was handed a golden opportunity to snatch a point when it was awarded a 93rd-minute penalty after Reina was harshly judged to have fouled Kouamé but the 37-year-old keeper saved Schone's spot kick.