Smalling scored for the third consecutive away Premier League match when he slid in Jesse Lingard's cross on 28 minutes.
Callum Wilson went close to a leveller for AFC Bournemouth, but he couldn't turn in a Joshua King centre from close range, under pressure from Luke Shaw.
And United made the match safe when Romelu Lukaku slotted in from Paul Pogba's 70th-minute cross, shortly after coming on as a substitute.
The Red Devils have moved four points clear of Liverpool in second place, and Chelsea, in fifth, are 14 points adrift with five matches remaining.
AFC Bournemouth remain 11th with three matches left.
AFC Bournemouth: 28 Apr v Southampton (A)
Man Utd: 29 Apr v Arsenal (H)