The Red Devils are now four points clear of Liverpool in second place with four games left to play, and head into their FA Cup semi-final with Tottenham Hotspur with a little momentum back on their side.
There was plenty of focus on Jose Mourinho's teamsheet before the match, which showed seven changes from the shock 1-0 loss to West Bromwich Albion last time out - Alexis Sanchez and Lukaku among those to make way.
In a quiet opening quarter the the contest, Bournemouth winger Jordon Ibe dragged wide from the edge of the box in the only sight of goal at either end of the field.
United finally upped things as the half-hour mark approached, coming close through a drilled Marcus Rashford shot moments before Smalling edged his side in front with his second goal in three outings.
Bournemouth's response in the remainder of the first half consisted of a weak shot on target from an off-balance Ryan Fraser and a more powerful drive from Joshua King that David de Gea could only parry.
For the first time in seven away matches United had a goal to show for their first-half efforts, although they still had work to do as the Cherries had conceded first in seven of their last eight matches here without losing any of them.
Bournemouth should have been given a chance to level things up less than 10 minutes into the second half, as Callum Wilson was stopped from meeting King's cross by Luke Shaw - the full-back getting a hold of his opponent on what was a rare start.
Phil Jones was also fortunate to get away with a pulling infringement in the box, with the game soon being broken up by a flurry of challenges.
Rashford, shifted into a wide position to compensate for Lukaku's introduction, cut inside and tested Asmir Begovic as United closed in on a second goal.
Bournemouth, now with one win in six top-flight meetings with United, were left with it all to do 20 minutes from time when Lukaku raced on to Paul Pogba's through-ball and clipped it over Begovic to kill things off.
Despite having the best record in the division from losing positions, the hosts could not muster a response as they fell to a fourth defeat in 16 since Boxing Day.
BOURNEMOUTH (4-4-1-1): Begovic; Francis, S.Cook, Ake, Daniels; Fraser, L.Cook, Surman (Gosling 75'), Ibe (Mousset 56'); King (Defoe 82'); Wilson
MANCHESTER UNITED (4-3-3): De Gea; Darmian, Smalling, Jones, Shaw; Herrera (Matic 72'), Fellaini, Pogba (Blind 80'); Lingard (Lukaku 62'), Rashford, Martial