Mick McCarthy's men remain unbeaten under his stewardship and have now won six consecutive games.
It's a second straight defeat for Jonathan Woodgate's side, who find themselves in seventh place and behind Cardiff on goals scored.
Story of the match
Bournemouth made three changes from Saturday's defeat at Queens Park Rangers. Captain Steve Cook returned from injury and replaced Chris Mepham, while Diego Rico and Sam Surridge came in for Jack Wilshere and Long.
McCarthy unsurprisingly named an unchanged side for the visitors following their emphatic 4-0 win against Preston North End.
The Cherries controlled the possession stats with 69% in the first half but could not create many chances against a well-disciplined Cardiff.
Cardiff went ahead in the 28th minute with their first effort on target. Former Bournemouth man Harry Wilson delivered an excellent corner, which was headed in by Morrison.
After being denied twice by Asmir Begovic before doubling their lead, Moore had a chance to beat him from the penalty spot when Perry Ng fouled Rico. He made no mistake, with his emphatic spot-kick leaving the Bosnian helpless.
Rico’s cross found Surridge in the 41st minute, but Phillips made an instinctive save to deny his point-blank attempt.
The hosts introduced Long and Arnaut Danjuma at the break as they looked for a way back into the game.
Woodgate's men continued to control the ball in the second half and were more threatening after the changes.
Phillips expertly denied Stanislas from inside the box in the 57th minute and kept out his 25-yard free-kick moments later.
Cardiff made two changes an hour in and lost their shape, with Sheyi Ojo and Leandro Bacuna on for Wilson and Josh Murphy.
Bournemouth's substitutes combined six minutes later to give them a lifeline. Stanislas surged forward after a sloppy pass by Marlon Pack and found Danjuma. His blocked shot reached Long, whose close-range header beat Phillips.
Looking most likely to equalise, Stanislas came close again when he sent a free-kick onto the roof of the net.
Chances were scarce in the final stages of the game. Bournemouth's last opportunity fell to Danjuma after a one-two with Stanislas, but his effort was saved comfortably by Phillips.
Man of the match
The Cardiff shot-stopper made some vital saves to ensure his side came away with three points. His save to deny Surridge before half-time was a pivotal moment in the game, as Bournemouth may well have got something had it gone in.