Ghosal defeated Pakistan's Iqbal Nasir 11-6 9-11 11-2 11-9 in a contest, which lasted 58 minutes at the Yeorumul Squash Courts.
Dipika, on the other hand, triumphed in an all-Indian battle against senior pro Joshana Chinappa 7-11 11-9 11-8 15-17 11-9.
Ghosal, the 28-year-old Asia number one, took control of the proceedings quite early and barring a minor slip, he was clinical in sealing the issue in his favour.
"Won my match 3-1 today! I had to be really solid against a very determined opponent :)," Ghosal tweeted after the tie.
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The women's match turned out to be a pulsating contest as expected. In a roller-coaster battle, Joshana clinched the opening game 11-7 in just nine minutes but Dipika bounced back to draw level.
Dipika then went on to notch the next two games before the two girls got locked in a nerve-wrecking battle in the fourth game. Joshana led 10-8 but Dipika pulled things back and the two went neck-and-neck till 13-13.
However, Dipika did not give up and fought back brilliantly to outwit Joshana 11-9 in the decisive fifth game.
Both Joshana and Dipika had called the draw "unfortunate" and the former had even considered a pullout claiming "manipulation".
India has so far won four medals (all bronze) at the Asian Games since the sport was introduced in the 1998 Bangkok edition. Two of them have come courtesy Ghosal and the rest in men's and women's team event.