This is the first-ever Fed Cup meeting between the two countries in the best- of-five matchup.
McHale was scheduled to play against newly-crowned world No. 1 star Victoria Azarenka, who is coming off her first-ever Grand Slam title at the Australian Open, but the 22-year-old Belarusian withdrew from the match earlier in the day with a lower back injury.
The American teenager instead faced off against Anastasia Yakimova and easily dispatched her 6-0, 6-4.
McHale was up 4-0 in the second set before Yakimova won the next four games, but McHale rallied to take the next two and the first rubber for the U.S.
Yakimova committed eight double faults in the match and hit 27 unforced errors, while McHale converted on 6-of-8 break opportunities in the nearly 1 1/2 hour match.
The former No. 1 American Williams came on next and battled through the first set against Olga Govortsova before rolling in the second to earn a 7-5, 6-0 victory.
Govortsova converted on her lone break chance in the first set, but also committed seven double faults and 19 unforced errors. Williams then dominated the second set despite hitting 14 unforced errors.
Sunday's reverse singles in Massachusetts will pit the U.S. Open runner-up Williams against Azarenka, who is still eligible to compete if healthy, and the New Jersey native McHale versus Govortsova, while the doubles currently call for an American duo of Venus Williams and Liezel Huber to battle a Belarusian pairing of Azarenka and Govortsova on Day 2.
The winner here will advance to the World Group playoffs and have a chance to compete for the Fed Cup title next year.