Patrick, the first woman to start the race on pole, went into the final lap in third place but fell back five places as Jimmie Johnson held on for victory ahead of Earnhardt Jr.
Patrick, who crashed out early in her debut last year, had the highest finish ever by a woman, bettering Janet Guthrie's 11th place from 1980. She also became the first woman to lead the race.
"She's going to make a lot of history all year long," said Earnhardt, who finished second for the third time in four years.
"It's going to be a lot of fun to watch her progress. Every time I've seen her in a pretty hectic situation, she always really remained calm."
A marketing dream for the sport and her sponsors, the 30-year-old Patrick is proving wrong her doubters, who wondered if she had the ability to deal with the challenges of stock car racing's premier event.
She never fell below 12th in the 200-lap race.
Earnhardt Jr, who has a huge fan base and whose father is one of NASCAR's all-time greats, who died from a crash in the 2001 Daytona 500, says he sees the necessary qualities in Patrick's driving.
"She's got a great level head. She's a racer. She knows what's coming. She's smart about her decisions. She knew what to do today as far as track position and not taking risks.
"I enjoy racing with her. Look forward to more all year long. It's just going to be a lot of fun having her in the series."
Patrick was more modest in her assessment of her own performance and disappointed with the end to her bid.
"I would imagine that pretty much anyone would kick themselves," she said, reviewing how she was unable to make the most of her third place and even improve it in the race's closing laps.
"I didn't know what to do exactly. So I feel like maybe that's just my inexperience. Maybe that's me not thinking hard enough, I don't know, (not) getting creative enough.
"I definitely was a little uncertain how I was going to be able to do it," she said.
Five-times NASCAR Sprint Cup winner Johnson said Patrick's racing style was well suited to her but warned she may find it tougher at other venues on the circuit.
"She's really comfortable in the car. Being close to other competitors, door-to-door, at these speeds, she was very comfortable.
"I think the style of racetrack really suits her. When we get to the other tracks, she has a steep learning curve ahead of her.
"But she continues to show her ability to drive race cars.. She made history today and in fine fashion, too".
(Editing by Gene Cherry)