McCoy had equalled Pipe's record with the appropriately-named On The Record at Uttoxeter on Wednesday, and went one better as the Jonjo O'Neill-trained 2-1 market leader It's A Gimme claimed the feature event of the day at Market Rasen.
The perennial champion jockey cut a confident figure throughout the two-and-three-quarter-mile Listed event and slowly eased his mount into contention heading down the back straight.
Following the victory the Moneyglass man was looking forward to a "satisfying call" to Pipe.
McCoy said: "I was lucky Jonjo had a few in the race and put me on this one. This is a willing little horse, who kept finding for me.
"The record was just a very personal thing between me and Mr Pipe.
"He set the standard and revolutionised training. He is someone I held in high esteem and we had great times together in my time as his stable jockey.
"We've had a bit of banter pretty much since I've ridden my 4,000 winner.
"It's only a personal thing and I will be putting in a satisfying call tonight."
McCoy was presented with a 20kg Lincolnshire Poacher cheese by the racecourse management in honour of his achievement.
Following McCoy's win, Martin Pipe described the 40-year-old as an "inspiration".
He added: "He's marvellous for our sport and it's just great we've got someone like him.
"Now, he's finally beaten me. All of us in racing are so proud of him for doing it."
McCoy went on to make it win number 4,193 when scoring on Parlour Games for John Ferguson in the B Eyre & Son Ltd Ford Novices' Hurdle at the race event.