Saido Berahino, Youssouf Mulumbu and Victor Anichebe struck for Alan Irvine's men, who completed a second straight win over the Republic despite JJ Koval's 73rd-minute goal.
While the 1-0 victory on Monday was unimpressive, West Brom were better in the second win as they defended well and kept possession to be more threatening in the attacking third.
Andre Wisdom, on loan from Liverpool, started for West Brom, who were again too good for a team in the third tier in the United States.
The hosts created the first decent opportunity as Max Alvarez, threatening in the first meeting between the teams, forced Ben Foster into a good save from close range.
Just moments later and the Premier League side were ahead.
Berahino was teed up just outside the area before finding the bottom corner with a volley in the 13th minute.
Steven Evans had a strike cleared off the line by Mulumbu before the Republic were punished for switching off again.
A bad turnover of possession led to Berahino squaring to Mulumbu, who side-footed a shot into the top corner from just inside the area.
West Brom were in complete control after going 2-0 up and could have added a few more goals before the break.
The Republic came out with more energy after the break but conceded again in the 62nd minute, when Anichebe fired into the top corner from 25 yards.
Koval tapped in for Sacramento after a header came off the post following a corner as the hosts got a consolation goal.
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