Anderson, who came up with a breezy unbeaten 39 off 22 balls to help Delhi Daredevils reach 188/6, also picked the crucial wicket of South African hitter David Miller to switch the momentum in favour of the hosts at the Feroz Shah Kotla on Saturday.
"As a bowler, you have to read the game. Zaheer sets some interesting fields and he's a smart cricketer. It's a nice confidence to have. It was a clinical performance from the bowlers," Anderson, who was adjudged the Man-of-the-Match said after the tie.
Commenting on the nature of the wicket, which hosted its first Indian Premier League (IPL) 2017 match, Anderson said: "It was the kind of wicket where it was tough to get going. Sanju (Samson) and Sam (Billings) set a great platform."
"It was good to have that platform to go from. We thought 160 might have been a reasonable target during one of the time-outs and in the end it probably was."
Asked about the changes in playing XI in every match, he said: "It's valuable to be able to chop and change combinations. Finding the right people to do the job is key."
Punjab skipper Glenn Maxwell conceded that his bowling unit needs to step up if they are to make a mark in the tournament.
"We were a bit behind with the bat. We probably gave 30 too many in conceding 188," he said.
"We let ourselves go and gave them too many boundary balls at the back end. We're not executing well enough with the ball. We failed in all three facets of the game today."
The Australian, however hailed the efforts of all-rounder Axar Patel, whose 29-ball 44 helped them reduce the deficit of the loss besides picking the key wicket of Daredevils' top-scorer Billings with his left-arm spin.
"Axar continues to show he's a superstar and Cariappa did well too," he added.
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