Connolly and Ondrej Palat gave the Lightning a 2-0 lead before the game was seven minutes old. Stamkos gave the Lightning a three-goal lead before Connolly scored again at 18:41 of the second period by weaving his way through a pair of defenders and beating Carter Hutton, who allowed four goals on 17 shots in two periods.
Connolly, the sixth player taken in '10, is battling for one of the open roster spots after spending last season in the minors.
"I saw two goal-scorer's goals," Lightning coach Jon Cooper said, "and we saw a lot of that in the second half of last year [in the American Hockey League]. He's [been] doing it in camp, and been doing well."