The hosts were also fortunate late in the half when Signe Bruun bundled the ball into the England net but the goal was disallowed for a handball.
Parris, who recently moved to Champions League winners Olympique Lyon, helped to settle the team's nerves in first-half stoppage time when she pounced on a poor clearance at the edge of the box and her shot crept past goalkeeper Katrine Abel.
Skipper Scott made it 2-0 with a header from close range in the 59th minute after she made an unmarked run from midfield to get on the end of Beth Mead's cross.
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England play one more warm-up game against New Zealand on June 1 before heading to France for the World Cup where they will begin their campaign in Group D against Scotland on June 9 before taking on Argentina and 2011 champions Japan.
(Reporting by Rohith Nair in Bengaluru; editing by Clare Fallon)
