Colombia was playing for the first time in the World Cup, and before Tuesday's game reserve goalkeeper Yineth Varon was suspended for failing drug test taken Saturday.
Landstrom, the player of the match, had a number of chances but scored from close range off a fine cross by Lotta Schelin on the right wing.
"We won our opening match. It's been awhile since that last happened," Sweden coach Thomas Dennerby said.
The Swedes kept Colombian star 17-year-old Yoreli Rincon in check, but Colombia coach Ricardo Rozo said he expects more from her as the tournament progresses.
"If she goes on working properly she can show more than she showed today," Rozo said. "Look at this girl — she wants to be the best player in the world and she's working on it!"
He refused to comment on Varon's suspension.
The game was played before a crowd of 21,106 at Bay Arena. Neither team was at its best in the draining humidity and 90-degree heat.
"We prepared ourselves in the best way possible," Landstrom said. "We knew it was going to be warm weather, so there's nothing we would have changed."
Schelin created drama in the second minute when she beat Colombia goalkeeper Sandra Sepulveda, only for her shot to be cleared off the line by Natalia Gaitan. Moments later, Caroline Seger set up Schelin, whose shot was parried by Sepulveda and cleared off the line again despite a defensive mix-up between Andrea Peralta and Colombia captain Gaitan.
Landstrom had a terrible miss in the 13th minute — after the ball was played back by Schelin — when she missed from close range.
Colombia took a while to settle in, then displayed good individual technique despite physical challenges from the Swedes.
"Of course we have to use our physical preconditions," Dennerby said. "Use whatever you have."
After Landstrom scored, Carmen Rodallega nearly tied it in the 66th when her shot landed on the top of the net. Therese Sjogran came close before substitute Sofia Jakobsson drew a good save from Sepulveda in the closing stages.
"Perhaps we should have scored two or three more goals," Dennerby said. "But it doesn't matter today. We won. It was an excellent opening match, both physically and mentally for us."
Rozo preferred to look to a promising future for women's soccer in Colombia.
"We have lots of young players rising through their academies and they're going to grow," Rozo said. "We feel perfectly comfortable here."