Norm Van Brocklin holds the record with 554 for the Rams in 1951.
Schaub completed his final 16 passes in regulation time to rally the Texans.
Johnson caught 14 passes for 273 yards, both career highs; the yardage was a team record. The Texans (9-1) won an overtime game for the first time at Reliant Stadium.
Chad Henne threw a career-high four touchdown passes in relief of injured Blaine Gabbert for the Jaguars (1-9). First-round pick Justin Blackmon finally had his breakout game, making seven catches for 236 yards. It was the first time in NFL history opposing players each had more than 200 yards receiving in the same game.
Blackmon caught Henne's pass at midfield, shrugged off two defenders for a stunning 81-yard touchdown with 12:33 left in regulation to put Jacksonville up 34-20.
Schaub then threw two touchdown passes to tight end Garrett Graham in the final 5:39 to force overtime.
Shayne Graham and Josh Scobee kicked field goals in overtime and, for a while, it looked like NFL would have its second tie in two weeks. San Francisco and St. Louis finished 24-24 last week.
Henne threw incomplete on fourth-and-10 from the Houston 47, and the Texans regained possession with 2:30 left in OT. Schaub flipped a screen pass to Johnson, who sprinted untouched down the right sideline for the winning score.
The Texans improved to 2-7 in overtime in their history, while the Jaguars dropped to 0-3 in OT this season.
Gabbert left in the first quarter with a bruised right elbow. Henne looked much more effective against the Texans.
Playing for only the fourth time this season, Henne barely beat a Houston blitz with a throw to Blackmon for a 63-yard gain, then found tight end Marcedes Lewis in the end zone late in the opening period. The Texans hadn't allowed a touchdown since their 43-13 win over Baltimore on Oct. 21.
The Jaguars had 238 yards in the first half, just 26 yards shy of their average output this season.
Henne started the second half with a 39-yard throw to Blackmon, then found Blackmon again to convert a third down to the Houston 30. Scobee kicked a 40-yard field goal to put Jacksonville up again, 20-17.
Arian Foster fumbled and Schaub threw an interception as the Texans looked like they might get embarrassed at home after beating Chicago at rainy Soldier Field last week.
Schaub was flawless in leading the Texans back, though, and Houston had a chance to escape in regulation, but Graham badly hooked a 47-yard field-goal attempt at the end.
The Texans finished with 640 total yards.
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Texans 43, Jaguars 37
Jacksonville 7 10 10 7 3 37
Houston 7 10 3 14 9 43
Hou • Martin 9 pass from Schaub (S.Graham kick), 12:15.
Jac • Lewis 13 pass from Henne (Scobee kick), 2:56.
Jac • Shorts 67 pass from Henne (Scobee kick), 12:31.
Hou • Casey 1 pass from Schaub (S.Graham kick), 7:52.
Jac • FG Scobee 43, 2:53.
Hou • FG S.Graham 42, 1:12.
Jac • FG Scobee 40, 11:01.
Jac • Lewis 1 pass from Henne (Scobee kick), 6:52.
Hou • FG S.Graham 27, 2:15.
Jac • Blackmon 81 pass from Henne (Scobee kick), 12:33.
Hou • G.Graham 1 pass from Schaub (S.Graham kick), 5:39.
Hou • G.Graham 5 pass from Schaub (S.Graham kick), 1:34.
Hou • FG S.Graham 25, 8:10.
Jac • FG Scobee 33, 4:21.
Hou • Johnson 48 pass from Schaub, 2:01.
Attendance • 71,676.
First downs 17 39
Total Net Yards 458 640
Rushes-yards 29-86 35-136
Passing 372 504
Punt Returns 2-11 2-76
Kickoff Returns 6-149 5-162
Interceptions Ret. 2-35 0-0
Comp-Att-Int 18-35-0 43-55-2
Sacked-Yards Lost 2-6 2-23
Punts 5-48.4 3-37.0
Fumbles-Lost 1-1 2-1
Penalties-yards 6-54 2-20
Time of Possession 31:19 41:40
Rushing • Jacksonville, Parmele 24-80, Henne 2-7, Jennings 3-(minus 1). Houston, Foster 28-77, Forsett 7-59.
Passing • Jacksonville, Henne 16-33-0-354, Gabbert 2-2-0-24. Houston, Schaub 43-55-2-527.
Receiving • Jacksonville, Blackmon 7-236, Shorts 3-81, Lewis 3-40, Parmele 3-3, Spurlock 2-18. Houston, Johnson 14-273, G.Graham 8-82, Daniels 6-57, Walter 6-54, Casey 3-20, Foster 3-15, Jean 1-11, Martin 1-9, Forsett 1-6.
Missed Field Goals • Houston, S.Graham 50 (WL), 47 (WL).