MIAMI, June 2 (Ticker) -- When Dwyane Wade came down with the flu, the Miami Heat had to be feeling a bit queasy. In the end, however, the Detroit Pistons were left feeling sick to their stomachs.

The Heat are headed to the NBA Finals for the first time in franchise history, overcoming Wade's untimely illness with a huge game from Shaquille O'Neal and hot shooting from Jason Williams in an affirming 95-78 victory over the Pistons.

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The second-seeded Heat won the series in six games and ended the two-year reign of the top-seeded Pistons as Eastern Conference champions. They play at Dallas or Phoenix on Tuesday.

"To be at the point where we are now on our way to The Finals is truly amazing for this organization," Wade said. "As the saying goes with this team, they did what they do and we went out there and played team basketball at the right time of the year."

"I only celebrate when it's really over," said O'Neal, who is headed to The Finals with his third team. "I'll celebrate a little bit, but like I told the guys, the job is not done."

Miami avenged last year's disheartening loss, when it held the lead with less than two minutes to play in Game 7 at home but was denied by Detroit. Wade labored through that game with bruised ribs.

A sickening case of deja vu swept over South Florida when Wade missed Friday's shootaround - and briefly was hospitalized - with a bad touch of the flu. He showed courage in starting and playing 37 minutes but was not himself.

"At 3 a.m. is really when I woke up and I knew I wasn't going to go back to sleep," Wade said. "My wife was giving me tea and vapor rub and everything she could. I told her to call our trainer, probably 7 or 8 today, and that's when he told me I needed to get to the hospital. I stayed at the hospital until 3 p.m. They I went home and changed and came to the game."

"I feel bad for him after what he had to go through in last year's playoffs," teammate Antoine Walker said. "He got hurt ... last year and to see him not at 100 percent was tough. We felt for him but we were very confident that we could pick up the slack and make it happen."

Wade didn't have to be 100 percent, not with O'Neal unleashing a "Shaq Attack" and Williams finally finding his shooting touch. The Heat took the lead for good in the first quarter and took off in the third period, when Wade finally got into the act.

O'Neal scored 28 points on 12-of-14 shooting, grabbing 16 rebounds and blocking five shots.

"Shaquille is Shaquille. We couldn't get him the ball enough," said Heat coach Pat Riley, also going to The Finals with his third different team. "We couldn't straight post him up, so we started doing a lot of things to move him a little bit on pick-and-rolls so he could get the ball."

"I just told the guys that they can come to me. Whenever they need a bucket just come to me," O'Neal said. "For the first five or six minutes, I actually didn't touch the ball and I got a little worried, but everyone else was playing so well, I just became a role player - until they came to me."

Williams made his first 10 shots before missing his last two, finishing with 21 points.

"I think you saw his game tonight," Riley said. "It was at the right time, there's no doubt."

"I just wanted to come out and try to do what I always try to do - be aggressive and knock down open shots, and luckily they were falling for me tonight," said Williams, who was shooting 38 percent in the postseason.

Wade had 14 points and 10 assists. He began as a playmaker, missed the start of the second half to take fluids and scored Miami's last eight points of the third quarter to open a 72-53 lead.

"(O'Neal) just told me to come in and just pace myself," Wade said. "He said the guys are ready today so you don't have to do it all today. Just pace yourself. I did that, and when it was time for me to take over, I went out there and hit a couple shots."

The Pistons had been 11-2 in elimination games over the last four years, including 3-0 this season. But they could not muster up another season-saving effort as they were thoroughly outplayed, perhaps signaling a changing of the guard in the East.

"Well, I think we had a great year," coach Flip Saunders said. "Ultimately, there's failure for 29 teams and success for one team, and that's pretty much how you judge it."

Richard Hamilton needed 28 shots to score 33 points for the Pistons, who won a franchise-record 64 games during the regular season with crisp chemistry but lost their edge in the playoffs when they began bickering a bit.

"It hurts," Hamilton said. "At the end of the day, if you don't win that ring, all what you did all season don't mean nothing."

Amid all the analysis, what this series came down to was making shots. In the clincher, Miami shot 56 percent (39-of-70) while Detroit managed just 33 percent (27-of-81).

"Every time we crawled back, we got open shots but just didn't hit them," Pistons forward Tayshaun Prince said. "I can't remember the last time we played defense like this. When you play defense like this and you give the other team a chance to set up their defense, that is when we became cold."

In the first quarter, the Heat made 10 straight shots - none by Wade. Williams and O'Neal sank four apiece before a 3-pointer by Walker made it 25-16.

The Pistons hung around, closing to 42-36 with a 9-2 run capped by a 3-pointer from Rasheed Wallace with 2:18 left in the first half. But they did not score again before the break, and O'Neal's tip-in helped rebuild the lead to 47-36.

In the third quarter, Wade was late coming out of the locker room and O'Neal had to sit down with his fourth foul. It didn't matter to Williams, who drained a pair of jumpers and a 3-pointer to push the margin to 64-49.

"The guys have been on my back, telling me to stay aggressive and they're going to fall, and tonight they did," Williams said.

Wade finally announced his presence, making four straight jumpers to close the quarter.

"If anything, (the fluids at halftime) helped me just trying to get hydrated," Wade said. "That's why I came out a little late. I was still getting my IVs in me trying to get hydrated."

Hamilton scored 12 points in the first five-plus minutes of the final period to cut the deficit to 80-67. But his drive was blocked by O'Neal, who scored at the other end. Williams added a jumper for an 84-67 bulge with 5:13 left, starting the party at American Airlines Arena.