The Seahawks (6-9) have scored 143 points in their last five games and won three times. Prior to that, Seattle averaged just 18.1 points in its first nine games.
"We knew we could do this all season long," Seattle wide receiver Koren Robinson said. "We just had to get it open and have everybody start making plays. We're cooking right now. Everyone is making their plays."
Alexander rushed for 79 yards on 24 carries and his second touchdown was his team-record 17th. Chris Warren set the club mark with 16 touchdowns in 1995 and Alexander matched it in 2000. Alexander's second touchdown of the game -- a one-yard run with 8:58 remaining in the third quarter -- gave Seattle a 20-3 lead.
Of Alexander's 15 rushing touchdowns, six have come in his last five games.
Hasselbeck completed 20 of 32 passes and has thrown for 1,903 yards and 11 touchdowns over his last six games.
"I'm happy for him," Seattle Coach Mike Holmgren said. "When we brought him in, I thought he could play. But he is way more than just my guy. He has to be his teammates guy and I don't think they ever lost faith in him.
"He has played pretty well in these few weeks that he has been the starter to the point to where I think our offense has a lot of confidence."
"He has more confidence in me now than earlier in the year," Hasselbeck said. "If he thinks that we're good enough to make those plays, then he'll call them."
Hasselbeck has had three 300-yard games since replacing Trent Dilfer eight weeks ago and the Seahawks are 5-4.
It took just 3:07 for the Rams (6-9) to lose Marc Bulger.
Bulger, who was trying to become the first quarterback to win his first seven starts since Minnesota's Daunte Culpepper in 2000, suffered a back injury when he was sacked by Antonio Cochran and John Hilliard.
Bulger had completed 64 percent of his passes for 1,815 yards with 14 touchdowns and six interceptions in six games before Sunday.
But he attempted just one pass before Cochran hit him in the legs and Hilliard hit him in the back.
Bulger was taken to a local hospital where a CAT Scan revealed no fracture. He will undergo further tests when the team returns to St. Louis.
Jamie Martin came on and completed 31 of 48 passes for 259 yards. But he threw two of his three interceptions to safety Reggie Tongue.
Rams coach Mike Martz blamed himself for being unable to adjust to Bulger's injury and was troubled that his running game produced just 17 yards.
"I had a hard time adjusting when Marc went out," Martz said. "It shocked me and I don't think I adjusted very well. I didn't help the quarterback that much. He got in a rhythm and got going pretty good, but the thing that bothered me more than anything was our inability to run the ball."
Linebacker Anthony Simmons had Seattle's first interception, which he returned 15 yards to the St. Louis 43. Four plays and 2:17 later, Alexander broke the record.
Torry Holt, who had 10 catches for 107 yards, got St. Louis within 20-10, when he caught a five-yard touchdown with 9:17 left in the third.
In the first half, Lindell booted field goals of 36 and 31 yards. Alexander's first touchdown upped Seattle's lead to 13-3 with 8:43 left in the first half. Alexander's score was set up by his 25-yard run and Rams cornerback Dexter McCleon's facemask penalty.