Daniel Sturridge scored a delightful strike from outside the area in the first half to put Liverpool a goal to the good.
Liverpool have been pressing Stoke hard for much of the first half but the Potters were woken up by the England striker's opening goal of the Premier League season.
Luis Suarez made an appearance on the Anfield pitch before kickoff, but failed to make Brendan Rodgers' final squad.
Iago Aspas was given a first Premier League start by Rodgers, while Stoke City boss Mark Hughes included Wilson Palacios in his starting XI.
"We're Stoke City! We play on the floor!" was the chant from away fans throughout the game as the Potters impressed with their new style of play.
But it was only Asmir Begovic who prevented Liverpool from racking up a cricket score, with the Bosnian turning on a masterclass of goalkeeping on the day.
However, it was Mignolet on his Reds debut who was the decisive keeper after he saved Jonathan Walters' 88th minute penalty. Dan Agger was judged to have handled across, but Mignolet saved his blushes by turning aside Scouser Walters' spotkick.