Goals from Vusumuzi Vilakazi and Kagisho Dikgacoi handed the hosts all three points and saw them move into the top four of the League table, while Ezenkosi continue to struggle in the first half of the 2007/08 season.
Cosmos goalkeeper Avril Phali was twice called upon to make fine saves in the first 20 minutes; first at his far post in the third minute from an Arrows corner, before producing a fine reaction block from Philani Shange's deflected effort.
The visitors also had their early chances, but both Gerald Mtshali and Dikgang Mabalane failed to test DR Congo goal minder Miphy Lupini.
The impressive Ugandan Geofrey Massa did call Lupini into action with a powerful shot just past the half hour mark but the 'keeper was equal to the task, blocking the effort at his near post.
Phali again had to react well just before half time when Valery Nahayo's attempted clearance rebounded off Shange and looped toward goal, but the 29-year-old 'keeper palmed the ball over his crossbar to the leave game goalless at the interval.
Just ten minutes after the break, Arrows finally broke the deadlock with a superb team goal. A slick passing move ended with Norman Smith back-heeling the ball through a mass of bodies to set up Vilakazi for an easy finish past the left hand of the helpless Phali.
Nahayo and Lucky Mhlathe were both forced into clearing off their own goal line in the 65th minute as Arrows laid siege to the Cosmos defence.
Abafana Bes'thende's pressure finally paid off with just over 15 minutes to play, as Dikgacoi scored a fine individual goal, moving strongly down the left channel of the penalty area before firing into the top corner of Cosmos' goal, albeit with a deflection off Mtshali.
Substitute Sehlolo Nale almost added to Arrows' tally in the 81st minute, forcing Phali into a fantastic save with a powerful drive that seemed destined for the top corner.
The win lifts Arrows up the table on 19 points, while Cosmos remain near the bottom on 12 points.