Breaking Haase to love, Federer confirmed the double break of serve for a 5-1 advantage when the Dutchman sent a forehand long.
Petchey said: "I think the most impressive and inspirational thing is he is the guy who has everything".
Federer, whose glittering career has re-ignited since taking six months off in 2016, has won three of the last five grand slams having gone five years without one.
In Sunday's final in Rotterdam, the 36-year-old Federer will win his 97th career title if he beats Grigor Dimitrov, dubbed "Baby Fed" early in his career for his style similarities with the Swiss great.
And Federer, now a four-time world number one, who holds the record for most weeks at the top with 302, believes this achievement outstrips the other times he held the title of best male player on the planet.
Yet it is the Alpine nation's favourite son, Roger Federer, who has apparently mastered the art of reversing it.
Federer triumphed 6-3 7-6 in the Rotterdam Open semi-final a day after reaching the summit of the ATP rankings again.
The second was a much more competitive affair, with neither player offering a sniff on serve.
Agasi wrote on his twitter handle, "36 years 195 days" Roger Federer has been increasing the level of our game.
From one legend to another.
Andre Agassi was 33 when he set the previous oldest mark back in 2003. There is grace and glide and nothing looks so tough. "I just didn't just get it by Rafa losing somewhere or dropping points or me sitting on the sidelines like in 2012 when I was on holiday and got the ranking two weeks after Wimbledon".
Just about 15 minutes later, the match-and Federer's quest for the top ranking-was concluded.
Federer at the start of the season he defended his victory in the Australian Open and closed the gap on Rafael Nadal to 155 points. Earlier this record was in the name of Nadal. After, such an amazing run, the opportunity to be the World No.1 again presented itself to Federer at the ongoing Rotterdam Open. It was a horrible moment, not just for the man himself, but for spectators present at the scene and those watching far and wide.
As a talented junior, Federer's on-court tantrums and hair-trigger temper threatened to stunt his progress.
Despite his achievement, Federer still has a semi-final to play on Saturday.
Age, after all, is only a number.
Men may come and men may go, but the GOAT goes on for ever.