The hard-hitting, Miami-based Puig
, ranked 65th in the world, battered the Italian to win 6-3 6-2 on Court 18.
Errani, a finalist at the French Open last year and a semi-finalist there earlier this month, said she had let her fear of grass get to her.
Though she saved six match points, she ran out of puff and answers to the relentless attacks of the 19-year-old Puig, who reached the third round of the junior event here in 2010 but had never played a senior grand slam before this year's French Open.
"My biggest problem is moving, in that I'm afraid of hurting myself so I can't move as I would like," Errani told a news conference. "It is difficult to get rid of the fear - you can't go to the gym and come out and it's better.
"I'm afraid of falling on the ground and getting an injury," added Errani, who did fall flat on her face to give away a point in the second set, and who had pulled out ahead of last week's Eastbourne grasscourt tournament to rest an injured muscle.
Puig, who said fans in Puerto Rico had woken up early to watch her match live on television, told reporters she had two sources of inspiration - the men's game and defending Wimbledon champion Serena Williams.
"I look to the men's circuit because there is so much more consistency," Puig said.
"I try to use (Serena) as an example on the court, the way she conducts herself and just the aura that she brings on to the court," she added.
"She intimidates the opponents and she is just able to maintain that level through the whole match."
Puig goes on to play unseeded Spaniard Silvia Soler-Espinosa while Errani lives to fight another day albeit as one half of the top-seeded doubles team with compatriot Roberta Vinci.
(For more sports news and updates, follow Ahram Online Sports on Twitter at @AO Sports and on Facebook at AhramOnlineSports)