Victorino, who signed a three-year, $39 million free-agent deal with Boston during the off-season, delivered a two-run single in a big second inning that staked the Red Sox to a 4-0 lead.
The outfielder capped the scoring with another RBI hit during a three-run ninth as the Red Sox spoiled the Yankees' 2013 home opener.
Jacoby Ellsbury went 3-for-6 with two RBI while Jose Iglesias added three hits, including a run-scoring single, en route to the victory.
Jon Lester (1-0) went five innings for the win, yielding two runs on five hits while walking two and striking out seven.
Yankees starter CC Sabathia (0-1) was touched for four runs on eight hits over five full frames.
Francisco Cervelli drove in both New York runs.