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.
The Baggies ran out 1-0 winners on Monday and improved on that showing the second time out, with Andre Wisdom, on loan from Liverpool, making his debut against the third-tier American side.
Despite the difference in class, it was the hosts who 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.
However, the the Premier League side were ahead just moments later as 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 turnover in possession in midfield 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 added to their lead in the 62nd minute, Anichebe firing into the top corner from 25 yards.
There was still time for the hosts to grab a consolation goal, however, as JJ Koval tapped in for Sacramento after a header came off the post following a corner.