The Canadian Tuft, of Orica-GreenEdge, triumphed in the 19.2km stage with a time of 22 minutes and 14 seconds to take his first victory of the season.
Tuft finished seven seconds in front of his closest rival, Argentine Leandro Messineo (San Luis Somos Todos).
Polish rider Kwiatkowski crossed third 11 seconds behind Tuft, which was good enough for him to snatch the lead off Brazilian Alex Diniz (Funvic Brasilinvest), who has now dropped to fourth at 45 seconds off the pace.
The 35-year-old Tuft won the stage on the back of three individual time trials victories in 2012, a duo time trial with team-mate Luke Durbridge and two team time trials.
The seven-stage event continues on Friday with the 169km Juana Koslay-Carolina stage and finished on Sunday in Juana Koslay.