Cabrera finished 4-for-5 with three runs scored.
Torii Hunter rapped out three hits, reaching the career 2,000-hit plateau as the Tigers took the opener of a three-game series.
Alex Avila added a solo homer for Detroit, which was coming off a weekend series win against the New York Yankees.
Anibal Sanchez (1-0) earned his first victory of the season, limiting the Blue Jays to two runs on five hits while striking out eight through seven innings.
Toronto, meanwhile, fell to 2-5 to begin the year as Brandon Morrow (0-1) was tagged for five runs on nine hits in just 3 2/3 innings.
Colby Rasmus socked a solo homer for the Blue Jays.
2014: The Year in Music [PHOTOS]