On the score-sheet for United was Pogiso Sanoka with a first half goal, with Mohau Mokate, Andrea Fileccia and Evans Rusike all firing in goals in the second stanza.
Maritzburg started the game brightly and there were early half chances for Siyanda Xulu and Sanoka.
Lebohang Maboe then fired a shot over the bar before Evans Rusike failed to hit the target with an attempted chip as the KZN team continued to dominate.
The breakthrough came in the 38th minute when Maboe picked out Bevan Fransman at the far post, who headed the ball back across goal where Sanoka arrived to steer in a cleverly-directed header of his own.
There was another chance for United just before half time when Ndlovu's stinging drive from an angle drew a smart save from Celtic keeper Patrick Tingyemb.
The second goal came just two minutes after the interval and from a beautifully crafted move as Siphelele Ndlovu played in Maboe, whose low cross was turned in from close range by the ever-willing Mohau Mokate.
The cushion of a second goal enabled Maritzburg to take the sting out of the game, the Team of Choice showing good game management to wear down an increasingly dispirited Phunya Sele Sele side.
Maritzburg's night got even better when substitute Andrea Fileccia snuck in to convert Bandile Shandu's cross with his very first touch of the game after being sent on by coach Fadlu Davids 15 minutes from time.
Rusike should have made it 4-0 a few minutes later, but blazed over the bar from close range.
But after Yazid Atouba was denied by Tingyemb, Rusike struck in spectacular style three minutes from time when he drilled home a low shot from the edge of the box to make it a memorable evening for the Team of Choice faithful who had turned out in their numbers on a balmy evening in Pietermaritzburg.
Maritzburg: Ofori, Sanoka, Fransman, Xulu, Makaringe, Shandu, Maboe, Ndlovu, Mekoa, Mokate , Rusike.
Subs: Mpandle, Onyango, De Reuck, Matima, Atouba, Fillecia, Ntshangase.
Celtic: Tignyemb, Pfumbidzai, Rikhotso, Ndengane, Letsoalo, Maema, Gordinho, Baloyi, Hotto, Mabena, Phalane.
Subs: Chaine, Lubisi, Maruping, Mashikinya, Nyundu, Motshegwa, Dlamini.
FADLU'S MID-SEASON REPORT
COACH PRAISES PLAYERS’ EFFORTS
MARITZBURG ON FORM AGAINST BAROKA
FADLU CREDITS PLAYERS FOR CHARACTER, PERSEVERANCE
SECOND HALF BLITZ SECURES VICTORY
MOKATE WANTS TO MAKE UNITED FANS SMILE AGAIN
GOALS A SHARED RESPONSIBILITY - FADLU
FADLU'S REPORT ON BIDVEST WITS DRAW