The British number two had not won a singles contest since before the Australian Open, but the 26-year-old overcame the disappointment of squandering several match points to beat her Ukrainian opponent by a 6-3 3-6 7-6 scoreline.
With a large percentage of her ranking points to defend over the grass-court season, Watson is effectively playing to keep her place in the world's top 100, and taking the opener against Bondarenko suggested an upturn in fortunes.
However, the world number 73 dropped the second set and struggled to hold serve during the decider, but so did Bondarenko who denied Watson a chance of victory on multiple occasions during the closing stages of the third.
Watson dug deep, however, as she overturned a 2-1 deficit in the tie-break to take it 7-3, completing the triumph in two hours and 38 minutes.
Fanny Stollar will stand in Watson's way in the second round.