The No.10-seeded Errani was a game away from losing the first set trailing 5-4, but she flicked the switch at just the right moment, winning five games in a row - and eventually nine of the next 10 - to close her fellow former Top 10 player out in straight sets in an hour and 34 minutes, 7-5, 6-1.
"The first round is never easy and the draw is especially strong here," Errani said. "Andrea is always a very tough opponent and very competitive - and we played very close in the first set, obviously.
"I didn't play my best, but it's okay. The goal was to win and keep going in the tournament."
Errani has quite a bit to defend over the next few weeks - she was a semifinalist at three big events in a row last year, first here in Madrid, then Rome, then Roland Garros - but she's already buffered those with a semifinal finish in Stuttgart two weeks ago, and this is her very favorite surface, after all.
"It's nice to be on clay again," the Italian No.1 said. "Of course it's a lot of points to defend, and a lot of pressure, so it's not going to be easy, but I'm happy to be back on clay and I'm happy to be here.
"I love Madrid. And I love Spain, it's my second home, and I have a lot of friends here."
There were five other winners on Day 1 of main draw play, most notably home favorite Garbiñe Muguruza. While Spanish No.1 Carla Suárez Navarro was winning the first WTA title of her career over in Oeiras, Muguruza - Spain's No.2 player - rallied from a set and 3-0 down and battled almost three hours to beat Sílvia Soler-Espinosa in an all-Spanish clash (read more about that match here).
Other matches saw Alison Riske let two set points go in the first set but beat Kaia Kanepi, 6-7(7), 6-1, 6-2, Bojana Jovanovski rout Karin Knapp, 6-1, 6-1, Magdalena Rybarikova close out Annika Beck, 6-2, 7-5, and Christina McHale beat Lauren Davis, 7-6(2), 6-3 (read more about that match here).
Bencic, who beat Camila Giorgi in her final round of qualifying match, is slotted to play No.1 seed Serena Williams in the first round on Sunday. The 17-year-old Swiss, who was recently profiled on CNN Open Court, filmed a video from the Mutua Madrid Open too - watch it at the top of this article.