Watson, 22, was broken in the opening service game on the Grandstand Court, and following some more wild returns soon found herself 4-0 down inside 15 minutes as the first set ran away from her with some 20 unforced errors.
However, Watson used the rest period to compose herself, inflicting an early break on the world No 96 in the first game, which set the tone of the second set.
Rodina had beaten Watson, ranked 41 in the world, in their previous two matches – first in 2010 on clay at Dothan and then in 2011 in Memphis, and she returned to the WTA Tour last year following the birth of her daughter.
However, Rodina, 26, was soon trailing 5-1 as Watson consolidated her advantage with another break before holding to love in game six.
The Briton levelled the match after another long return by the Russian, with both players then taking the opportunity of going off court for the bathroom break.
The heat continued to sap both players??? energy levels, but Watson recovered composure to hold her serve and then consolidated a break to lead 5-2.
Rodina then offered stubborn resistance to win the next three games, with Watson left frustrated after a somewhat controversial call from the umpire going against her.
The British No 1 was not to be denied, however, holding serve to lead again at 6-5 and then converting a first match point when Rodina’s return hit the top of the net and dropped just wide.
Watson, who reached the fourth round in Indian Wells earlier this month, will now face world No 15 Angelique Kerber of Germany.