Mason Robertson's neat header in the 18th minute put the visitors in the driving seat before Gnohere Krizo converted a penalty in the 57th minute to wrap up the three points.
Both sides came into the fixture on the back of defeats and in a bid to snap out of the downward spiral that they find themselves in, either coach made three changes apiece.
Arrows got their first opportunity in the 11th minute when Manvir Singh tried his luck from distance only to see the ball going out of bounds. Mason Robertson broke the deadlock against the run of play when he leapt above his marker to convert a looping cross from Brian Mascarenhas in the 18th minute.
In the 40th minute, the Indian Arrows survived another scare when Gnohere Krizo brushed aside two defenders with some finesse, leaving Hendry Antonay and R Hormipam at bay before pulling the trigger but his attempt agonisingly hit the woodwork as Real Kashmir settled for a solitary goal advantage going into the break.
After the breather, Ayush Adhikari had a crack on goal from about 30 yards in the 50th-minute but an alert Phurba Lachenpa produced a fingertip save, much to his defence's relief.
David Robertson's side were awarded a penalty in the 57th minute after Bikash Yumnam was adjudged to have handled the ball inside the box. Gnohere Krizo stepped up and made no mistake from twelve yards to double the advantage.
A Givson Singh free-kick in the 80th minute was the closest the young Arrows got to pulling one back, but the Snow Leopards held on to end their three-match winless run. The Srinagar outfit climb to seventh in the Hero I-League table, having nine points to show for it while the Indian Arrows still remain rooted to the bottom.
( With inputs from IANS )