The 24-year-old batsman batted with confidence to score 41 on his debut and then 38 in the second as England won both matches in Dubai to take an unbeatable 2-0 lead.
Vince vowed England would not be complacent and would go for a 3-0 win.
“To come here and win 3-0 would be a great effort, that’s what we’re looking to try and do,” said Vince, who added he enjoyed his first chance in Twenty20.
“I was included in the squad last summer, but didn’t get the chance to play. So it’s nice to come out here and get an opportunity. I’m enjoying every minute of it.
“I am staying on for another three or four weeks to play Pakistan A, so that will be another tough series,” said Vince of England Lions’ series with Pakistan’s second string in the United Arab Emirates next month.
“I get the chance to captain the Lions, so that will be another good experience,” said Vince.
“I’d love to play all formats. My first chance has come in Twenty20. I hope I can push on, find my way into the 50-over side – and the Test side as well, I hope.”
Vince admitted he was nervous in the first match on Thursday.
“I was nervous walking out that first game, in front of a full stadium, but I settled down after a couple of balls and eased into it nicely,” he said.