Butt scored 135 off 143 balls with 14 fours while Asif took 2-22 as they led the Water and Power Development Authority to a convincing 141-run victory over Federally Administered Tribal Areas in a one-day cup match in Hyderabad.
"I hope that this is the new beginning," Butt said. "As long as I will get more matches, I will improve."
Both players were eligible to compete from last September when their bans ended but first had to go through the Pakistan Cricket Board's rehabilitation program.
Asif, Butt and fast bowler Mohammad Amir were banned for at least five years for deliberate no-balls at a 2010 test match against England. Butt was captain of the team for the Lord's test.
Amir pleaded guilty from the onset, which accelerated the left-arm fast bowler's return to the national team, Butt and Asif went on to challenge the bans until their appeals were rejected by the Court of Arbitration for Sport.
Both players ultimately accepted their responsibility before the ICC lifted their bans.
The PCB agreed a six-month rehabilitation program for the duo that included lectures to younger cricketers on anti-corruption before allowing them to compete in domestic matches.
"I am very relaxed, the toughest phase of my life is over," Asif said.
"This one-day tournament will help me gauge where I stand ... International cricket is my target but I have to do well in the domestic matches before I can hope (for) international cricket."
Pakistan coach Waqar Younis said last week that, if they perform well in domestic matches, both players deserve another chance in international cricket.
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