Suni Chhetri opened the scoring for Grayson's side in the 57th minute from a close-range header from a corner. Javi Hernandez doubled the lead for the home team in the 70th minute.
Deepti finished with figures of three for 15 and became the first Indian to take 100 T20I wickets at Newlands as her side took a giant stride towards the knockout stages.
The second Test of the series will be held in Delhi's Arun Jaitley Stadium from February 17 to 21. India have 1-0 lead in the Border-Gavaskar Trophy series
The Gaurs sit in sixth position of the league table and would be looking to secure the three points which will bring them closer to a seat in the top six.
Bengaluru FC will be looking to consolidate their place in the top six with a win against the shield winners Mumbai City FC. The Blues are in the fifth spot with 28 points in the ISL standings.
After bagging an important three points, Hyderabad FC confirmed a second-place finish in the league table with two games remaining. Meanwhile, ATK Mohun Bagan continue to remain fourth on the points table, only one point above seventh-placed Odisha FC, with 28 points from 18 games.
A late Bartholomew Ogbeche winner meant Hyderabad FC not only went home with three points, but also secured second place in the ISL standings. They now have 39 points in the bag after 17 games. Meanwhile, the Mariners remain in the fourth spot with 28 points and drop further down in the race
Morale is high for a Bengaluru FC side that extended their winning streak in the ISL to six games this past weekend, their longest-ever streak. A much-needed victory against arch-rivals Kerala Blasters FC handed the Blues the bragging rights and lofted them back up into the playoff spots.
The 26-year-old sat out India's opening group match, a seven-wicket win over Pakistan, due to a finger injury. But India's star opener appears set to return for the clash at Newlands having come through a pre-match training session unscathed.
When the team stepped out from Airport only Kuldeep Yadav and Ravichandran Ashwin came out along with coaching and other staff members. Even the head coach Rahul Dravid was not there with the team.