Anderson marked his 100th cap in grand fashion, removing Marlon Samuels to level Botham’s mark of 383 and then becoming a record-breaker in his own right when Denesh Ramdin edged to slip in the evening session.
Anderson celebrated English cricket’s new magic number of 384 in ecstatic fashion, sprinting up the pitch with arms outstretched before leaping in joy as his team-mates swarmed.
As well as his personal milestone, Anderson had forced the door ajar for his side, who needed three wickets to win the game in 18.4 overs.
But the hosts closed on 350-7, the impressive Jason Holder scoring a vital 103 not out, with No 9 Kemar Roach hanging in as the overs evaporated.
England’s final chance came and went six overs from stumps when James Tredwell just failed to gather a return catch that had looped off the leg of Yorkshire’s Gary Ballance at silly point.
The result means England have still not won an away Test since Kolkata in December 2012 and go to the second Test in Grenada all square.
But once that disappointment passes, this will go down as Anderson’s hour.
Since his arrival on the Test stage as a punk-haired 20-year-old, he has experienced the highs and lows of international sport and come through it as a master of his art.
Only 13 players have ever taken more Test scalps than him and it was fitting that both his wickets came from a stand named after one of them – Sir Curtly Ambrose.
Botham paid tribute to “awesome” Anderson, saying he feels that the Lancashire player is the “complete bowler”.
“He has been a joy to watch for more than 12 years in an England shirt and I’m absolutely delighted for him that he has finally overtaken me to be No 1 on the Test wicket-takers list out on his own,” Botham wrote. “He has been out on his own for years as the leader of England’s attack and the finest swing bowler of his generation.
“He hasn’t done it the easy way, he has had to work hard for his rewards and he has had to improve along the way to become the complete bowler he is today.
“You don’t take as many wickets as he has by being a one-trick pony who can only succeed in swinging or helpful conditions.”
Botham feels Anderson can reach another milestone.
“It has been a privilege to watch him up close all these years and commentate on a career that I believe still has a few more miles in the tank yet,” he said. “I expect him to go past 400 now and set a record for the ages.
“And I’m glad I was here in Antigua to watch him do it. I’ve got a rather large gift for him waiting for him to open back at home, but in the meantime I’ll be sharing a glass with him at some point and having a chat about his fantastic achievement.”
Anderson’s first Test captain Nasser Hussain said: “I’m very proud of him. It’s an incredible moment really.
“The work he’s done behind the scenes, the hard times he’s had, he’s reaping those rewards.’’
Hussain sensed from the outset that Anderson was a huge and unique talent in English cricket.
“When I first saw him, and gave him that first England cap, I knew he was probably the most skilful bowler we would produce,” he said. “He had something like a young Pakistan bowler. He knew his game – it was all about swing, it was raw ... getting the ball down there, and getting wickets.
“He always had the skill. I think he’s developed physically, mentally, got through those hard times.”
Immediately after his achievement, Twitter was full of compliments for Anderson.
“Congrats to the Dingle @jimmy9 England and Lancashire best ever !!,” said his former Lancashire and England team-mate Andrew Flintoff.
“Brilliant work by @jimmy9 to surpass Sir Ian Botham as our leading Test bowler. So proud of my mate. Really happy Cooky got the catch too”, added retired England spinner Graeme Swann.
Yorkshire’s former England captain Michael Vaughan commented: “A joy to watch @jimmy9 #384 #Legend #RecordHolder”.
Another former Yorkshire and England player, Darren Gough, simply stated: “Well done @jimmy9, truly deserved, a genius,” while the White Rose’s current first-team coach Jason Gillespie added: “James Anderson – take a bow! Congratulations! #well done.”
Former England wicket-keeper and captain Alec Stewart said: “Huge congratulations to @jimmy9 on becoming England’s leading Test wicket taker. Brilliant achievement. Next target 500 wickets please.”