Denmark's Caroline Wozniacki, Azarenka and Russia's Nadia Petrova, ranked 8-10, also received first-round byes.
But four byes finally took the tourists to victory after 94 minutes of play.
Newcastle and Middlesbrough, who were also relegated into the Championship, received byes for the first round.
The umpire at the bowler's end makes decisions on lbw decisions, no-balls, wides and leg byes.
Both Spaniard Moya and fourth-seeded Grosjean had had byes in the first round of the claycourt tournament.
Belgians Kim Clijsters and Justine Henin, seeded one and two for the tournament, both received first-round byes.
Each week there are only 14-16 games depending upon the number of byes in a given week.
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Two balls later, two more leg byes off another Johnson delivery saw India home and sparked jubilant scenes.
With two minutes to go, event organizers whistled, and folks from Publicis, Euro RSCG and Omnicom-owned TBWAChiatDay, began their good-byes.
Jankovic will play fellow Serbian Ana Ivanovic in a battle of former world No. 1s after both were given first-round byes.
The umpires indicate no-balls, byes, leg-byes, wides, boundaries and sixes to the scorers, who keep a running total of the runs scored.
The umpires indicate no-balls, byes, leg-byes, wides and boundaries to the scorers, who are responsible for keeping a running total of the runs scored.
Safina beat Kuznetsova in last year's final and Monday's matches were their first in the tournament as the top eight seeds all received first round byes.
The two women above, top seed Victoria Azarenka of Belarus and Russia's Maria Sharapova, have both received first round byes for the tournament on the Gold Coast, which also hosts an ATP Tour event.
The former rules on lbw decisions, no-balls, wides and leg byes, while the latter assists with stumpings and run outs and may help on the question of whether a catch has carried or not if there is uncertainty.
The two French stars Tauziat and Julie Halard-Decugis, who are top seeds at Birmingham and met in the final of the DFS Classic last year, are both also in action on Tuesday after receiving first round byes along with fast-rising compatriot Nathalie Dechy.
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