The former Wimbledon finalist, looking to begin her resurgence on the women's tour after dropping to 87 on world rankings, recovered some of her best form in a convincing win. She shot to an early 3-0 lead in the first set, dropped serve on a couple of unforced errors then picked up momentum again and quickly closed out the set.
The first four games of the second set went again to serve but Bouchard was dominant again when she steadied and put her first serve in play.
Bouchard gained in confidence, sending down three unanswered aces and clinching the match against the 88th-ranked Brengle in 71 minutes. She will face either Alison van Uytvanck or qualifier Bibiane Schoofs in the second round.
Puig won the Olympic women's singles title in Rio de Janiero in 2016 while Mattek-Sands was the mixed doubles champion at the same games. Mattek-Sands hasn't won a singles match on the WTA Tour since May.
Meanwhile, American Lauren Davis, who won the singles title in Auckland in 2017 but needed a wildcard to reach this year's main draw, advanced to the second round with a 6-, 6-2 win over Spain's Lara Arruabarrena.
Tuesday's draw is highlighted by the first round clash of former World No. 1s Venus Williams and Victoria Azarenka and the first appearance of defending champion Julia Goerges.
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