The only goal came early in the game, and the visitors wasted several chances to add to their lead, against a home team missing key players Collins Mbesuma and Robyn Johannes through injury.
Muhsin Ertugral, playing against his former club, saw his team improve after the break, but they lacked the cutting edge and remain in 12th place on the log.
Ajax, meanwhile, move up to seventh place.
The game began with wayward long-range efforts from Jabulani Nene and Lebogang Manyama at either end, before the visitors went in front through Maluleka.
An error in midfield allowed Nhlanhla Vilakazi to capitalise and thread a the ball straight down the middle, flicked on by Brent Carelse, with Maluleka driving into the penalty area and lifting the ball into the left corner of the net for the opener.
At the other end, Philani Shange had a first strike on goal seconds before the interval, although it was straight at Sander Westerveld.
After the restart Muhsin Ertugral introduced experienced striker Katlego Mashego in a bid to spark some life into his attack.
Ajax continued to do most of the running and Arrows keeper Nkosingiphile Gumede was forced to dash off his line to thwart Carelse.
The 18-year-old goalkeeper then almost made a hash of a back pass that ran under his foot, although he managed to get back and kick the ball away.
With 20 minutes to go, Thamsanqa Gabuza managed to get the ball into the back of the net, but the strike was ruled out for off-side.
Mashego had a good chance seconds later, but stumbled at the crucial time, while Gumede blocked out Maluleka from point-blank range.
The Ajax goal-scorer was then called into action at the other end of the park, clearing on the line after Musa Bilankulu’s touch as the visitors held on for the win.