Philani Shange opened the scoring late in the first half before Thamsanqa Gabuza doubled the advantage in the middle of the second half.
The two goalkeepers were hardly threatened in the early stages of the first half with both sides failing to take advantage of the wide pitch at the Sinaba Stadium to stretch the defence.
Katlego Loke spotted Helton Da Rocha off his line in the 17th minute but the Arrows goalkeeper recovered in time to watch his lobbed attempt sail over the bar.
Three minutes later a cross found Dillon Sheppard inside the box and he took a first-time shot with his favourite left foot, but his shot lacked pace and direction and missed the target.
Lehlohonolo Nonyane went on a great run in the 29th minute, beating a couple of defenders as he burst into the penalty area only to see his final pass cleared by Robyn Johannes.
Two minutes later Loke latched onto a long ball and found himself inside the box with one defender to beat, but he opted to take a shot which crashed against the side netting.
The home side continued to press forward in search of the opening goal and fashioned another chance in the 39th minute with Tshidiso Tukane playing a great pass to put Matthew Rusike through on goal.
The Cosmos forward did well to test the goalkeeper from a narrow angle but his low shot was well-saved by Da Rocha.
Arrows broke the deadlock in the first minute of added time when Jabulani Nene played a perfect ball over the Cosmos defence to pick up a great run from Philani Shange who pushed the ball past the advancing Avril Phali, 1-0.
Jomo Cosmos were guilty of committing silly fouls in the opening minutes of the second half but they went unpunished as Arrows failed to make good use of the resulting set pieces.
Gladwin Shitolo tried to test the goalkeeper from long range in the 58th minute but he failed to control his shot and sent it wide of the top left corner.
Two minutes later coach Jomo Sono brought in Siyabonga Nontshinga, who recently earned his first international cap, and he made an immediate impact on the game as he got in ahead of the Arrows defenders but was unfortunate to see his shot hit the side netting.
Arrows doubled the lead in the 64th minute when substitute Siyabonga Nkosi played a well-weighted pass to find Thamsanqa Gabuza at the far post, and he made no mistake as he side-footed the ball into the back of the net, 2-0.
Jomo Cosmos tried to pull a goal back but were unable to penetrate through the determined Arrows defence, while the two-goal lead also gave Arrows the confidence to pass the ball around.
The closest attempt for Ezenkosi came in the 88th minute when Siyabonga Nhlapho fired a fierce shot from inside the box but his attempt went wide of the left upright and Arrows held on to win their second league match away from home.
Jomo Cosmos remain at the bottom of the log and still winless after eleven matches.
Jomo Cosmos (0) 0
Lamontville Golden Arrows (1) 2 (Shange 45 + 1’, Gabuza 64’)
Jomo Cosmos: Phali, Samb, Nonyane, Sono (Theletsane 60’), Berthe, Gaborone, Appiah, Mngomezulu, Rusike (Nontshinga 60’), Loke (Mkhwanazi 72’), Tukane
Lamontville Golden Arrows: Da Rocha, Zwane (Musonda 69’), Bilankulu,Johannes, Tom,Khuboni,Nene, Shange, Van Heerden, Sheppard (Nkosi 61’), Gabuza (Mashego 85’)