Raj anchored the Indian run chase with a 47-ball 56 which she made with the help of seven fours in the Group B match which was marred by unprecedented docking of 10 penalty runs on Pakistan.
This was a result of Pakistani batters running on the danger area during their innings.
India also avenged their narrow 2-run defeat under D/L method against Pakistan in New Delhi in the previous edition of the tournament in 2016.
While openers Ayesha Zafar and Nahida Khan fell for single-digit scores, Omaima Sohail and Bismah Maroof failed to convert starts into big knocks.
Dar was dropped on 15 and again on 29, and Maroof enjoyed some good fortune on 28 when a gentle top-edge spooned over the umpire's head but was allowed to drop to the ground after bowler and fielders left it to each other.
Pakistan were still not out of the woods as they could only reach 53 for 3 at the half-way stage but the sloppy Indian fielding allowed their two batswomen Dar and Maroof to gain in confidence.
It meant India effectively began their innings on 10-0 and Raj calmly recorded their fifty with successive boundaries in the eighth over.
She took full advantage, soon reaching her seventh T20 global fifty.
Hemalatha and Poonam Yadav finsihed with three wickets apiece for India, and there were two for Radha Yadav. "It was unprofessional on our part, after being warned, we still trodded (sic) on the danger area, it's something we need to work on, it hasn't happened for the first time, it happened previously during the Sri Lanka series as well", said Pakistan captain Javeria Khan. Kaur also stitched a 134-run stand with young Jemimah Rodrigues (59) to bail India out of trouble as they had lost a few early wickets.