Yuki was authoritative in his 6-2 6-2 6-3 drubbing of Michael Venus in the decider after Somdev levelled the tie with his 6-4 6-4 6-4 win over Marcus Daniell in the first match of the day.
It was a do-or-die situation for India when Somdev stepped on the court and the country's numero uno singles player ensured that India remained in the hunt.
Yuki, who was playing only his second live fifth rubber, came out all guns blazing against Venus, who had stunned Somdev in the first match of the tie.
The 23-year-old Delhi-lad turned out to be India's hero in this tie as he won both his matches. He had lost the deciding fifth rubber against Serbia's Filip Krajinovic in September in Bangalore last year.
Yuki stamped his class and authority right from the start and did not face a single break point till the sixth game of the third set.
Yuki asserted himself by breaking Venus twice in each of the first two sets, running away with a 2-0 lead.
It was in the third set that Venus threatened a bit when he had Yuki down a break point in the sixth game but the Indian was up to the task and thwarted his rival's attempts.
Yuki saved two more chances in the eighth game and finally converted his third match point to seal the tie for his side. India will now strive to make the World Group when they compete in the Play-offs in September.
Earlier, Somdev delivered when it mattered the most taming Daniell in two hours and 18 minutes to keep India afloat in the tie.
Daniell replaced Jose Statham, who was down with a flu, but could not help his side seal the tie.