“Gifted” is a simple, pleasant drama that engages the emotions without manhandling them. It depicts a child-custody battle yet avoids cheap melodrama and doesn’t paint anyone as a villain. It has the glistening falseness of a Nicholas Sparks weepy that bears only passing resemblance to real life, but you can caught up in its family turmoil — resolved peaceably, you may be assured — without feeling insulted.

Chris Evans stars as hunky loafer Frank Adler, a damaged fellow living in Florida and caring for his 7-year-old niece, Mary (Mckenna Grace), whose math-genius mother committed suicide 6.5 years ago. Mary is a math prodigy too, bored and sassy when Uncle Frank sends her to public school for the first time. Everyone tells Frank that Mary should be at an academy for smart kids, but that’s the route Mary’s mother took, and it made her unhappy. Frank is convinced that his sister would want Mary to have a normal childhood.

The person who doesn’t want that is Frank’s mother, Evelyn (Lindsay Duncan). A former math whiz herself before she got married, Evelyn is a no-nonsense Brit who’s had no contact with her granddaughter until now, when she sweeps down from her hoity-toity Boston home to sneer at her son’s lower-class lifestyle (she’s been estranged from him, too) and paint him as an unfit guardian. Evelyn, though not unkind, doesn’t have much personal affection for Mary, but she is motivated by love — love for her lost daughter, who died before reaching her full potential.

Directed by Marc Webb (“500 Days of Summer”) from a screenplay by Tom Flynn, the story plays out satisfyingly and, believe it or not, not too predictably, with earnest performances all around (including from Jenny Slate as Mary’s schoolteacher and Frank’s potential love interest, and Octavia Spencer as his neighbor and landlady). No wheels are reinvented, no new ground is broken, but it’s a suitable example of sentimental filmmaking done right.

B- (1 hr., 41 min.; PG-13, moderate profanity, brief mild sensuality.)