Watson will face compatriot and world No. 11 Konta in the second round after seeing off the American 4-6 6-2 6-2 on Wednesday.
The clash on Friday will be the first time the two have met on the WTA Tour.
Konta will go into the match as a heavy favourite against Watson, now ranked almost 100 places lower than her compatriot after dropping to 108 this week.
Watson paid the price for her rankings points from last year's title in Monterrey dropping off, and defeat by Gibbs would have seen her fall further.
But the 24-year-old kept her nerve and won 10 of the last 12 games, many of them tight, to clinch victory after an hour and 50 minutes.Reuse content