He couldn't win one years later, when, after years of mediocrity, he suddenly found himself back in the mix.
A win Saturday night at Lowe's Motor Speedway rocketed Burton onto Jimmie Johnson's bumper with five races to go to decide the championship, and Burton is convinced he's as capable of winning a title now as he was when he was a young hotshot.
"No one's ever proven to me why you can't do at 41 what you could do at 23," Burton said. "We're lucky to be in a sport that you can be successful in your 40s. You can convince yourself you're too old to do it. Trust me, a lot of people will try to convince you you're too old to do it.
"But with age comes a lot of advantages, too. And we'll try to take those advantages every chance we get."
Burton's peak started 11 years ago, when he started a string of five consecutive multiple-win seasons. In that period, he notched 17 victories and 102 top 10 finishes while slowly moving up in the standings.
He finished fifth in the standings twice, including his six-win season in 1999. He'd moved up to third in the final points the next season, and went into 2001 as the prohibitive favorite to win his first Cup title.
But Dale Earnhardt died on the final lap of the season-opening Daytona 500 that year, and many people believed it adversely affected the safety-conscious Burton. He became a proponent of industrywide improvements, and for the next several years became more known for his stances on safety than his on-track performance.
The wins dried up - he didn't reach Victory Lane from 2002 through 2005 - and left longtime car owner Jack Roush for a fresh start with slumping Richard Childress Racing.
Like Burton, RCR had fallen off following Earnhardt's death, and Childress needed new blood to help revitalize the program. Many told the car owner he was crazy to hire an aging driver who had failed to meet his potential and presumably lost his edge.
Childress didn't balk.
"Someone asked me a while ago about age, why I pick drivers - not in their golden years, but in their good years, as I call 'em," Childress said. "But Dale Earnhardt in 2000, we finished second (in the standings). I think he was 49. We were going to win the championship the following year.
"So age, like Jeff said, is only in your mind. If you take care of your body like Jeff does physically, your mind will be good."
Burton has proven that the past three seasons, steadily becoming relevant again.
He made his first Chase in 2006, and used a victory in Round 2 at Dover to take over the points lead. He stayed on top of the standings almost a month, then an engine failure at Martinsville sent him tumbling to fifth and opened the door for Johnson to win his first title.
Burton finished seventh, and can look back at that failed championship run and find what not to do this time around.
"It had been a while since I had been in the mix. So we were getting accustomed to all that again," Burton said. "As relaxed as we wanted to be, you know, I wasn't as relaxed as I thought I could be. I was saying all the right things, I was doing all the right things, I thought. But at the end of the day, I was still kind of tensed up about it.
"So lesson learned and we won't do that again."
This time he's relaxed, secure in his spot as an afterthought among the title contenders. Nobody predicted Burton would be a factor in the Chase - not after the stellar seasons Johnson, Kyle Busch and Carl Edwards had.
Burton had sort of hovered inside the top 12, never making a strong surge to the front. His win Saturday night moved him into second, gave him his first multiple-win season since 2001, and the confidence to make a run at the title.
"There's a lot that's going to happen between now and then," Burton said. "Everybody wants to give somebody a trophy right now. Just hold on for a little while. We're halfway through this thing. Anything can happen.
"And, by the way, it probably will happen."