Chelsea attacker Lauren James marked her first major tournament start with a sublime winner in the sixth minute, but the Lionesses were far from their free-flowing best once again and witnessed Keira Walsh sustain a potentially serious injury.
Following an underwhelming 1-0 triumph over Haiti in their opening group game, England boss Sarina Wiegman responded by promoting Rachel Daly and James to the starting XI, as Lauren Hemp and Jess Carter made way.
Daly took on left-back duties as James started up top, and Wiegman's decision paid dividends with just six minutes gone, as the duo combined for England's first goal from open play in the 2023 World Cup.
James dropped deep to receive the ball from Daly, and the 21-year-old drove forward before picking out the bottom corner with a delightful curling strike from outside the box, becoming the second-youngest England scorer at a Women's World Cup after Jill Scott.
However, England's efforts to add to their advantage proved fruitless, and Denmark were presented with their fair share of opportunities to restore parity by some sloppy Lionesses play, but profligacy also bedevilled the Scandinavians.
With seven minutes to go until half time, England were dealt another potentially devastating injury blow as Walsh was carried off on a stretcher with a knee problem, having appeared to overstretch while sliding in to make a tackle.
Laura Coombs came on to replace the stricken Walsh, but England remained relatively comfortable as the second half progressed, albeit while looking unlikely to double their lead.
Denmark were agonisingly close to levelling the scores in the 87th minute, though, as Amalie Vangsgaard was not picked up by a lethargic England backline and headed against the post from close range.
Wiegman's side held on for their second three-point haul of the World Cup, though, and the European champions will be through to the knockout rounds if China fail to beat Haiti this lunchtime.