The twin success took India's medals tally to five gold and two silver in the games.
Paulose clocked four minutes 22.56 seconds and finished comfortably ahead of second-placed Svetlana Lukasheva of Kazakhstan, who finished in 4:24.92. The bronze medal went to China's Li Zhenhu in 4:25.96.
The Indian girl was in control of the race right through and at no stage was her lead under any threat.
The 26-year-old Hamza, a bronze medallist at the Military World Games in Hyderabad two weeks ago, brought home a stunning result, beating more fancied Kuwaiti and Qatari runners.
Hamza hung in with the front-runners and broke off at the right moment to win in 3:50.22, a new meet record. Omar Al Rasheedi of Kuwait was a close second in 3:50.58 and Ali Kamal Abubakr of Qatar was third in 3:50.78.
The 24-year-old Sinimol, who runs both the 800M and 1,500M, completed a double of Asian Indoor athletics championships and Asian Indoor Games triumphs, as she had won the top spot in Asian Indoors in Bangkok last year.
Meanwhile, India's Bibin Mathew was knocked out of the 400 metres when he finished fourth in his heat in 48.83 seconds.
The race was won by Wang Lian Gyu of China in 47.86S.
Vinay Choudhary, another Indian entry, was also fourth in the second heat in 48.98s and was eliminated. Saudi Arabia's Hamdan Al Bishi clocked 47.98s to win the heat.
Results: Women 1500M: Sinimol Paulose (Ind, 4:22.56)1; Lukasheva Svetlana (Kaz, 4:24.92.3) 2; Li Zhenzhu (Chn, 4:25.96) 3.
Men: 1500M: Chatholi Hamza (Ind, 3:50.22) 1; Al Rasheedi Omar (Kuw, 3:50.58) 2; Kamal Abubaker Ali (Qat, 3:50.78) 3.
Kabaddi win
Four-time Asian Games kabaddi champions India continued their marauding ways, winning their second successive encounter.
In their second match on Wednesday, India outplayed Malaysia 65-22 after leading 30-8 at half time. On Tuesday, the Indians had trounced Sri Lanka 40-11.
The other teams in the competition are Bangladesh, Pakistan, Japan and Iran.
The seven teams will play each other once, with the top two clashing for the gold medal.
