Bush ran for 172 yards and two touchdowns, and the Dolphins won a home opener for the first time since 2005 by beating the Oakland Raiders 35-13.
Ryan Tannehill threw his first NFL touchdown pass, ran for another and avoided any turnovers after tossing three interceptions in his pro debut a week earlier.
The Dolphins improved to 1-1, and Joe Philbin earned a sideline drenching for his first victory as a head coach. The Raiders, under new coach Dennis Allen, are 0-2 for the first time since 2007.
''It was nothing fancy, nothing magical,'' Philbin said. ''Our identity right now is we've got to run the ball effectively and stop the run.''
Miami did both, outgaining Oakland on the ground 263-23.
Bush broke four tackles on a 23-yard touchdown run that put the Dolphins ahead to stay in the third quarter. After they forced a punt, Bush struck again, this time on a 65-yard scoring run.
Far from home on a sweltering afternoon, the Raiders wilted down the stretch. Miami employed a no-huddle approach most of the game and pulled away in the final 20 minutes by mounting touchdown drives of 80, 80 and 75 yards.
''We felt our tempo would be a key,'' Bush said. ''We pressed that tempo and felt like we wore them down and just continued to pound the ball.''
Carson Palmer threw for 373 yards, but the Raiders were plagued by poor field position and managed only one touchdown - when backup running back Mike Goodson took a swing pass and turned it into a 64-yard score.
Darren McFadden was held to 22 yards rushing and 19 receiving. The Raiders were only 1 for 12 on third-down conversions, and they had no takeaways.
''We haven't helped our offense out with field position,'' Allen said. ''We need to take the ball away and create short fields. We can't go 80 yards on every drive.''
Tannehill went 18 for 30 for 200 yards, including a 14-yard touchdown pass to Anthony Fasano. But the rookie's niftiest throw came as he was being tackled: Parallel to the ground, he side-armed a completion for a 3-yard gain.
He hit Brian Hartline nine times for 111 yards.
''We were able to establish the running game,'' Tannehill said. ''It takes a lot of pressure off.''
Bush had a career-high 26 carries and added three receptions for 25 yards. Lamar Miller carried 10 times in his NFL debut for 65 yards, including a 15-yard score to seal the victory.
The Dolphins trailed 10-7 in the third quarter before finally taking advantage of superior field position, when they had the Raiders pinned at their 1 and forced a punt that gave them the ball at the Oakland 44.
Four plays later, Bush scored the go-ahead touchdown either because of terrific balance or terrible tackling, depending on a spectator's point of view. He cut inside and ran through the arms of four defenders en route to the goal line.
His second touchdown came on a sweep, with Bush breaking into the open and dashing up the sideline. He leaped over the goal line as three defenders closed in, then raised his arms in jubilation.
The happy crowd chanted ''Reg-gie! Reg-gie!''
''It feels good,'' Bush said. ''I'm not going to lie and say it doesn't, to hear the fans cheering you on.''
The festive mood was a welcome change for the Dolphins, rebuilding after a third consecutive losing season and coming off their most lopsided season-opening loss since 1988.
''This game was huge for us,'' Bush said. ''We talked all week about bouncing back and just winning one game. This game is huge for our confidence.''
Miami started fast, taking The Opening kickoff and driving 80 yards in 12 plays for a touchdown. Tannehill scored untouched on a keeper around left end on third and goal at the 2.
Two possessions later, the Raiders went 92 yards for the tying touchdown, scored by Goodson. Oakland drove 81 yards in the second quarter for a field goal and a 10-7 lead at halftime.
But the Raiders didn't start a possession beyond their 20 until late in the third quarter, when Phillip Adams returned a punt 47 yards to give them the ball at the Miami 25. The Dolphins again dug in and forced a field goal.
''Obviously we didn't score enough points, and that's unacceptable,'' Palmer said. ''I put that on my shoulders. It's my job to find ways to get us into the end zone. I didn't do a good enough job today.''
NOTES: Raiders CB Shawntae Spencer sprained his foot in the second half, and RB Taiwan Jones hurt his ribs. ... Dolphins CB Richard Marshall left the game with a back injury. ... Oakland long snapper Jon Condo returned after missing practice during the week with a concussion. ... The Dolphins lined up for a 55-yard field goal try, and Dan Carpenter instead took a direct snap and kicked a pooch punt to the 8. ... Brandon Fields helped Miami's field position by averaging 53.2 yards per punt.