Rivers hit a wide-open Alexander on a 39-yard touchdown pass and Nick Novak added a 39-yard field goal to make it 13-0.
"We obviously don't have enough urgency, much consistency," Steelers receiver Mike Wallace said. "We have to pick it up. We have to."
Pittsburgh briefly rallied, getting across midfield for the first time during a last-second drive. Shaun Suisham made a 49-yard field goal at the halftime gun.
Any boost for the Steelers disappeared during the first 10 minutes of the third quarter, when San Diego converted five straight third downs during a 17-play drive capped by a 3-yard pass from Rivers to Floyd.
"Best drive of the year," Rivers said. "That one will be fun to watch over and over again."
The possession chewed 9:32 off the clock to give San Diego a 20-3 lead. The Chargers needed barely 10 seconds to put the game away.
Backed up yet again, Roethlisberger tried to hit Brown on a screen pass. It caromed off tight end David Paulson's rear and rolled into the end zone, where Quentin Jammer fell on it.
The play appeared to be overturned on review. Pittsburgh's offense ran back onto the field when referee Scott Green popped out from under the hood.
Instead, Green pulled a switcheroo, confirming the score to give the Chargers a 27-3 lead and a brief moment of joy in a year full of chaos.
Turner played like a coach who had nothing to lose. Late in the third quarter, leading by 17 and inside their own 30, the Chargers converted a fake punt when Eric Weddle took a direct snap for a 4-yard gain.
"One thing about our team," said Antonio Gates, "yeah, we've been struggling the last five weeks. But at the end of the day, it only came down to one or two plays in those games we lost. Today, we just were playing the way we were capable of playing, the way we know how to play.
"To do that and keep moving forward, that speaks a lot about this team and the character of this team."
NOTES: Steelers LG Willie Colon left the game with a left knee injury. Maurkice Pouncey moved from center to guard, with Doug Legursky replacing Pouncey at center ... Roethlisberger became the 25th quarterback in NFL history to surpass 29,000 yards passing and 1,000 career yards rushing ... San Diego WR Michael Spurlock had seven receptions for 64 yards, with five of the receptions turning third downs into first downs ... Steelers WR Plaxico Burress had an 18-yard reception in the first half, his first catch since being re-signed by the Steelers two weeks ago ... San Diego held the ball for 36:45, the most by a Pittsburgh opponent this season.
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