New Zealand looked poised to post a massive score after making 243-3 on the opening day of the second Test, but Babar and his fellow bowlers managed to bowl the Black Caps out for 403 late on Tuesday.
Hosts Pakistan negotiated 19 overs to close out the day 34-2 in reply.
Pakistan's four frontline bowlers have played just 18 Tests between them but Babar, who finished with figures of 4-137, believes they are performing as well as their more experienced predecessors.
"I got some confidence from the fast bowlers," said the 35-year-old. "When they were required to attack, they attacked.
"But the pitch was much better than the previous pitches we've had, in the series against Australia or the first Test against New Zealand.
"We really bowled as a team and worked together. If we wanted to contain them, we did, if we wanted to attack, we did it together.
"It was a great performance, especially because we are very new in Test cricket. Ehsan [Adil] hasn't played international cricket for a very long time, Yasir Shah has had a great start, he's only played three Tests.
"So I think even though we are very new, we bowled as well as our experienced bowlers did in previous series."
Babar and fellow spinner Yasir Shah (2-92) bowled more than 40 overs each in the first innings, but he said there was no danger of fatigue.
"I'm not feeling tired or anything so I'm okay with bowling so many overs," Babar said.
The way the guys are performing, we have performed very well in the last few games, so the momentum is very good. So I don't feel any fatigue or tiredness, I'm feeling fit."