Colorado's Jhoulys Chacin (0-2) had matched the Pirates' Charlie Morton (1-1) with scoreless frames until the fifth inning, when the Bucs erupted for five runs to put the game away.
After Nate McLouth and Andrew McCutchen each drove in runs, Jones golfed a pitch deep into the right-field bleachers for a two-run shot and Alvarez followed with a solo homer off the right-field foul pole.
Morton dominated Colorado on one run over seven innings, surrendering six hits and only one walk while striking out two for the Pirates, who bounced back from a 2-1 loss in Wednesday's first contest.
Chacin finished by allowing five runs on eight hits over five full frames.
Ramon Hernandez provided the only RBI for Colorado, which dropped the rubber match of a rain-delayed three-game set at PNC Park.