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Anderson has won 79 Test matches, the most of any England player, but said that this victory - with minutes to spare on the fifth evening - was among the best due to the placid nature of the pitch, which required bowlers on both sides to "dig deep".
"It's probably one of the best wins I've been involved in, if not the best," Anderson told Sky Sports. "On a pitch like that, to play the way we did, to score the runs at the rate we did, we gave ourselves a chance of getting a result and I think we deserved to put ourselves in that position at the end of the game.
"Today, it was an unbelievable effort from everyone. We tried so hard to get the ball reversing and doing something, going off the straight, and we created enough chances to get the win. It was hard, but we knew it was going to be difficult.
"With Ben [Stokes] and Brendon [McCullum], their mantra is that we've got to take wickets and look to take wickets all the time. Even though they [Pakistan] got 500-plus in the first innings, we still felt with that lead that we had, the way we scored, we could set ourselves something to defend.
"Coming into today, we knew it was going to be hard because it's still a good wicket but we managed to get the ball reversing which was absolutely huge. Getting the ball moving through the air makes a massive difference, and we executed our skills brilliantly."
Anderson returned second-innings figures of 4 for 36 in 24 overs, including the key wickets of Imam-ul-Haq and Mohammad Rizwan, but praised Stokes and Ollie Robinson for their burst with the new ball on the fourth evening.
"The one thing that stood out for me was the way that Ollie and Ben bowled with the new ball after not having much rest," he said. "They came out with that short-ball theory and it got us a couple of wickets early.
"That set things going and gave us a lot of confidence coming into today. We knew that it was going to be a big push and we dug deep today; we had to dig deep to try and get anything from that wicket."
Anderson described Stokes, the eighth captain he has played under, as an "incredible" leader. "He's someone you want to play for," he said. "He gives you so much confidence heading out there and the way he just knows what he wants to do.
"He thinks about it a lot: the fields that he sets and the way that he just tells you what to do, basically, is great for us. It's exciting, trying different things as well: exciting fields, different fields, thinking outside the box which you've got to do on pitches like this."
There are only three days between the first and second Tests of the series - the second starts in Multan on Friday - and Anderson admitted with a smile that he would feel sore on Tuesday after getting through 46 overs in the match at the age of 40.
"It's nice to have the win but I don't think tomorrow will feel great for me," he said. "It was a long five days. Quick turnaround, but that's the nature of Test cricket. You know coming into a series that you've got back-to-back games and have to recover well and then come back in three days' time and do it all over again."