The American hit a forehand and a backhand long before netting a crosscourt backhand to as Watson held serve to lead 3-0.
However after losing the first three games of the set, Williams steadied her game to reduce her error count to take the next four games to lead 4-3.
With Williams serving, Watson committed three groundstroke errors to put the American ahead 40-0.
Williams then struck a powerful 89 miles per hour forehand down the line winner to hold serve at love to lead 5-3.
With Watson serving to stay in the set, Williams hit another forehand down the line winner to lead 15-0 before several baseline errors from the Brit put Williams at set point at 30-40.
A double fault from Watson ended the set.
In set two, Williams continued to overpower Watson with the extreme pace of her strokes as she quickly went ahead 5-0 after winning her eleventh game in a row.
With Watson serving to stay in the match, Williams struck a powerful 78 miles per hour backhand down the line winner followed by a powerful forehand down the line return winner to lead 30-0.
However after Williams missed several additional powerful groundstrokes, Watson held serve to trail 1-5.
Serving for the match, the American survived three deuces before striking a swinging forehand volley winner to end the match.
In round two Tuesday or Wednesday (Monday or Tuesday night USA time), Williams will face either Caroline Garcia of France or Zhang Shuai of China.
The draw was not kind to Williams as she lost to Garcia last week at Wuhan in a third set tiebreaker and could meet the Wimbledon champion and last week’s Wuhan winner, the third seeded Petra Kvitova of the Czech Republic in the third round.
In the quarterfinals, Williams could face the the fifth seeded Agnieszka Radwanska of Poland. Should she continue to advance, Williams could then face her sister, the top ranked Serena Williams in the semifinals.