"We don't like to be in that situation, but we know if we stick together, we can pull games out," Posey said.
Dwyane Wade scored 31 points despite going 8-of-23 for the defending NBA champions, who improved to 2-2.
Reserve Dorell Wright had nine points, five rebounds and a career-high six assists.
"When Shaq's out, we know those other guys are going to be more focused and very determined," Watson said. "Hey, those guys won a championship, too."
O'Neal missed a second straight game because of a bruised left knee. Heat coach Pat Riley said X-rays and MRI results of O'Neal's knee were negative.
Wade's two foul shots with 53 seconds remaining pulled Miami within 86-85. Allen then hit one from the line to give Seattle a two-point edge with 34 left.
On the next possession, Posey nailed a 3-pointer from the left wing to give Miami an 88-87 lead.
"It's always good when the shots fall," Posey said. "It's about being in the right place at the right time."
"I just slipped. I don't know what it was," Wilkins said. "I can't say it was a wet spot. I just slipped."
Wade sank both free throws to give Miami a 90-87 lead. Wilkins missed a 3-pointer as time expired.
"There is a subconscious notion on the part of these guys that they don't have to prove anything until they have to prove it," Riley said. "That's lethal because we are not good enough to be that way and win."
The Sonics, who began a five-game road trip, scored well below their league-leading 111.7 points per game.
Haslem's eight points helped the Heat rally from a six-point halftime deficit to grab a 65-61 lead after three quarters. Watson and Allen then hit 3-pointers to spark a 10-1 run that gave Seattle an 81-75 lead with 6:29 left.
The Sonics fell to 1-3 despite leading late in each of their defeats.
"It's almost like we're afraid to win," Sonics coach Bob Hill said.
The Heat got a boost from Wright, who played in 23 games total during his first two seasons. He's getting playing time now partly because guard Jason Williams has been sidelined with a knee injury.
"I'm the youngest in here -- I should be the one with all the energy," Wright said. "I should be the one up and down the floor, getting the guys going."
Seattle led by as many as 12 points in the second quarter en route to a 46-40 halftime edge. The Sonics' reserves outscored Miami's subs 23-8 and the Heat shot 32.6 percent (15 of 46) in the first half.
Lewis scored 10 points to help Seattle build a 21-11 lead after one quarter. Miami was only 2-of-20, while Wade missing all of his seven attempts.
Miami beat Seattle for a third consecutive time for the first time ever. The Sonics lead the overall series 25-12. ... Lewis ran his career points total to 9,010. ... Seattle plays at Orlando on Wednesday night. Miami is off until playing at New Jersey on Friday.