The 19-year-old Archana beat a valiant Krittwika Sinha Roy 6-11 11-2 11-8 in the reverse women’s singles to clinch the issue for her side.
Delhi’s Sathiyan Gnanasekaran, world number 30, unexpectedly lost to Spain’s Alvaro Robles 1-2 in the reverse men’s singles.
He and Bernadette Szocs claimed the mixed doubles 2-1 but that was never going to be enough for his team after Amalraj’s win over Jon Persson.
Earlier, Romania’s Szocs put Delhi ahead in the opening women’s singles match, breezing past debutant Shruti Amrute 2-1.
Goa were dealt an early blow when their in-form player Cheng I-Ching, world number 9, was ruled out of the tie with high fever and Shruti was handed her UTT debut.
Amalraj, however, negated Delhi’s advantage by shocking Sweden’s Jon Persson 2-1. In a riveting contest, the two traded points all the way till 7-all in the first set. But Persson pulled away at that stage, taking all four points to wrap it up.
The mixed doubles was a much tighter battle, with fortunes rapidly swinging from end to the other. Sathiyan-Szocs jumped to a 5-0 lead, only to see Robles-Archana draw parity.
In the second set too, the Delhi pair felled behind 6-9, staring at a shock defeat. But Sathiyan played a couple of big shots to win it 11-9.
They stayed in control in the third, to wrap it up 11-8.