Kiplagat, 33, won the first gold of the Moscow world championships after taking control of the race in the shadows of the Luzhniki stadium to win in 2:25:44.
The smooth-striding Kiplagat, who led a Kenyan sweep of the medals in Daegu in 2011, stalked Straneo, 37, until the 40-kilometre mark after the two other leading protagonists — Japan's Kayoko Fukushi and Ethiopian Meselech Melkamu dropped off the pace.
Straneo, who underwent surgery in 2010 to have her spleen and gall bladder removed, was unable to keep tabs on the leader in the shade of the Olympic Park and took silver in 2:25:58. Fukushi secured bronze in 2:27:45.
Kiplagat's victory made up for a disappointing London Olympics last year when she was suffering with flu and trailed home 20th behind Ethiopian Tiki Gelana.
She showed she had regained her form by finishing second in the London marathon in April, but Gelana's poor season continued as she dropped out before the 15-km mark of a race run by the banks of the Moskva river and on a series of loops between the stadium and Red Square.
Gelana also suffered in the London marathon when was knocked to the ground after being struck by a wheelchair athlete mid-race, limping home in 16th place.