The Spaniard featured in three matches -- men's singles, men's doubles and mixed doubles -- and his side won all those games.
Frenchwoman Alize Cornet's 5-3 win over reigning US Open but retired Flavia Pennetta set the ball rolling for the Rangers as they handed Mumbai their second straight defeat.
Cornet featured in two wins -- women's singles and Mixed doubles -- for the Rangers.
Mumbai captain Richard Krajicek gave the hosts a perfect start with a 5-3 win over Thomas Muster in the Legends' singles but that proved to be the only set won by Mumbai.
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Next to follow was clash between Italian Pennetta and Cornet, who had stunned Venus Williams thrice in the 2014 WTA
season.
Cornet was the first player to hold serve in the fifth game after four consecutive break of serves and broke Pennetta one more time for a 4-2 lead. She eventually won 5-3.
Cornet then combined with Bautista Agut to take a 5-3 win the mixed doubles over the home pairing of Giraldo and Pennetta.
More shock was in store for the home team as Giraldo and national champion N Sriram Balaji lost 3-5 to Bautista Agut and Ramkumar Ramanathan. It was the Indian youngster who served bombs to take the set in the eighth game. The Rangers were leading 18-13 with one match to go.
Giraldo had to demolish his opponent if Mumbai had to win but Bautista Agut ensured that his side would seal the match with his solid game.
Giraldo saved a match point in an intense rally at 30-40 but buried a backhand to net next point as Agut won the match 5-2.