The British number two struggled on the American hard courts and in Asia but needed just 64 minutes to beat Belgian Wickmayer 6-2 6-1.
Watson took her chances impressively, converting all four break points, and won more than half the points on her opponent's serve.
She will face Estonian third seed Anett Kontaveit in the second round.
It was a good day for Britain, with Naomi Broady also through to round two after an impressive 6-2 6-2 victory over sixth seed Tatjana Maria.
The 27-year-old lost in the final round of qualifying to Pauline Parmentier but was given a lucky loser spot for the second successive week and this time took full advantage.
Broady lost just five points on serve during the match and dominated Maria's second serve to claim her first top-100 scalp since June.
In a repeat of the 2016 Olympics final, gold medallist Monica Puig once again defeated Angelique Kerber, this time 6-3 6-4 to send the tournament's top seed out at the first hurdle.
Eugenie Bouchard was eliminated despite winning the opening set against Johanna Larsson, but Sabine Lisicki and second seed Kiki Bertens both marched on.
Maria Sharapova suffered a first-round exit at the Kremlin Cup in her native Russia just two days after winning her first WTA title since returning from a drugs ban.
The 30-year-old was back on home soil for the first time since serving a 15-month ban for testing positive for the banned substance meldonium, but was ousted in straight sets 7-6 (7/3) 6-4 by Slovakian Magdalena Rybarikova.
Sharapova admitted that had this tournament not been in Russia, she would have skipped it having won the Tianjin Open at the weekend.
"I wanted to finish my season in Moscow - I haven't played here for 10 years and every year I try to qualify for the (year-ending) Championships in Singapore, it is an important big tournament, and that's the reason I play in my motherland so rarely," she said in quotes published on kremlincup.ru.
"If the tournament were held in a different city than Moscow, I wouldn't have played after five matches in China. I fought, I tried to do my best and tried to win this match but my opponent played well."
Fifth seed Anastasia Pavlyuchenkova was beaten 7-6 (7/2) 6-1 by Daria Kasatkina, but Julia Goerges dropped just three games en route to victory over Polina Monova and sixth seed Daria Gavrilova overcame Kristyna Pliskova 6-4 6-7 (5/7) 6-1.
Elsewhere, Irina-Camelia Begu, Vera Lapko and Natalia Vikhlyantseva were all victorious.
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