A 27-yard field goal by Ka'imi Fairbairn tied it with 1:34 remaining.
Two plays later Joseph stepped in front of a pass from backup Nathan Peterman intended for Kelvin Benjamin and dashed untouched into the end zone to put the Texans on top and help them avoid their third straight overtime game.
''I kind of thought for a second to just get there and hold the ball so we can the run clock out,'' Joseph said. ''But then I was like: `A chance like that (doesn't) come by so often. I've got to score this.'''
The Bills had a chance to tie after that, but Kareem Jackson intercepted Peterman with 35 seconds left to secure the victory.
Joseph's late-game heroics helped Houston to its third straight win on a day Watson committed three turnovers.
The Bills hurried and harassed Watson all day, sacking him seven times and hitting him 12 more. Watson, questionable this week with a chest injury, was slow to get up several times and didn't seem to be moving as well as he normally does.
Watson brushed off questions about his health, saying he didn't ''want to make any excuses,'' but his teammates acknowledged the injury and said it made them want to do more to help him.
''When you've got a guy that sacrifices everything when he's hurt, everybody around him better do the same thing, especially if it's your quarterback,'' defensive end Jadeveon Clowney said. ''I think everybody put that on their shoulders this week and just tried to give it all up for him.''
Watson was 15 of 25 for 177 yards with a touchdown and two interceptions. He also lost a fumble.
Peterman threw for 61 yards with a touchdown and two interceptions for the Bills (2-4) after taking over for rookie Josh Allen, who left with an elbow injury late in the third quarter. Allen threw for 84 yards and ran for 20.
Bills coach Sean McDermott said after the game that they were still evaluating Allen's injury.
He saw some good things from Peterman but was disappointed with his turnovers.
''At the end of the game ... he was probably trying to do too much,'' McDermott said. ''I don't want to paint it all bad, but we've got to protect the football and make sure we're smart.''
The Bills took their first lead of the game when Peterman found Zay Jones in the corner of the end zone on a 16-yard pass that made it 13-10 early in the fourth quarter.
Lorenzo Alexander tipped a pass by Watson at the line and intercepted it on the first drive of the second half. The Bills had a first down at the 8-yard line before their offense stalled and they kicked a 22-yard field goal to cut the lead to 10-3.
Peterman's first pass after taking over was incomplete and his second was short of a first down, and the Bills added a 52-yard field goal to get within 10-6.
Watson was sacked on Houston's next drive and Harrison Phillips recovered his fumble at the Houston 32 near the end of the third quarter.
The Texans recovered a fumble on a punt return and took advantage of the mistake a few plays later when Watson connected with DeAndre Hopkins on a 13-yard pass to make it 7-0. A 33-yard field goal pushed the lead to 10-0 in the second quarter.
Bills LG Vladimir Ducasse left in the fourth quarter with a knee injury. ... Allen looked to be in quite a bit of pain in the sideline as trainers worked on his elbow.
Houston's J.J. Watt had a sack to give him at least one in four straight games and leave him tied for the NFL lead with seven this season. Watt has played well in his return after playing just eight games combined in the previous two seasons because of back surgery and a broken leg.
''I'm just trying to get better and better,'' he said. ''Everybody told me I was washed-up. Some people didn't think I could get seven sacks on the season. I'm just trying to keep doing what I'm doing.''
Bills: Visit Indianapolis next Sunday.
Texans: Visit Jacksonville next Sunday.
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