Parris scored from the spot in the 14th minute and Ellen White added another goal for Phil Neville's side five minutes before half-time on the Cote d'Azur.
A shaken Scotland fought back in the second half, and Claire Emslie reduced the arrears with 11 minutes to go, but they could not find an equaliser.
The Lionesses will still feel they were worthy winners. Among the favourites to win this World Cup, they are now well set up to progress from Group D before facing Argentina in Le Havre on Friday and then returning here to Nice to tackle former winners Japan on June 19.
Neville - who resembled men's manager Gareth Southgate, sporting a waistcoat on the touchline - had warned that this would be his team's toughest fixture in the group stage.
However, at the Nice stadium where England's men lost to Iceland at Euro 2016 and which registered a crowd of just 13,188 for the occasion, Neville's team ultimately got the job done in the first half against a Scottish side playing their first ever match at the World Cup.
Shelley Kerr's team were determined to make this a contest after losing 6-0 when the sides met in their opening game at Euro 2017, and they did that, but it was ultimately to no avail.
They will protest that the early penalty decision that went against them conditioned the rest of this match, though.
Fran Kirby's cross flicked off the partially outstretched arm of Nicola Docherty inside the box. Czech referee Jana Adamkova was alerted to the possible handball by the video assistant and pointed to the spot after a review.
Parris, who recently agreed to join European champions Lyon from Manchester City, duly smashed the penalty past Lee Alexander in the Scotland goal.
Scotland had set themselves up to frustrate England, but were now left chasing the game on a warm and sticky evening. Crucially, they conceded again with half-time approaching.
Captain Rachel Corsie came to meet Kirby on the edge of the box but did not get to the ball, which fell for White to slot in.
White earlier had the ball in the net only for the offside flag to cut short her celebrations, and Beth Mead also had a goal ruled out at the start of the second half.
With Alexander excelling, Scotland ensured the final scoreline was nothing like as chastening as two years ago in the Netherlands.
Unlike in 2017, they had the experience of Arsenal's Kim Little and Jen Beattie in their line-up too, as well as lively young Chelsea forward Erin Cuthbert.
They kept playing and got a goal back in the 79th minute.
Steph Houghton's pass out from the back was intercepted, allowing Lisa Evans to set up Emslie, with the player who has spent the last two years at Manchester City forcing the ball home, but England held on.