Victory would leave England 2-0 up in the four-match encounter with just the final Test, at The Oval later this month, to come.
Pakistan now have to score 323 to level the series after Strauss's 116 was the centrepiece of England's second innings 345 on Monday.
Only two sides in history have won a Headingley Test after scoring more than 300 in the fourth innings and Strauss said: "I would make us just favourites."
The opening batsman, whose side are chasing their first home Test series victory against Pakistan since 1982, added: "The wicket should only probably get worse tomorrow (Tuesday) and we saw today (Monday) there was probably a little bit more uneveness with the new ball.
"Either way, one team is going to have play well to win it and hopefully it's us," insisted Strauss, who oversaw England's crushing innings and 120-run second Test victory at Old Trafford.
"From our point of view there's enough in that wicket for us to believe there are 10 wickets out there
"But there's a pretty small margin of error for bowlers. If they do get in the right spot, it's very hard work for batsmen. If they don't, there are runs to be had."
Recalled England wicket-keeper Chris Read, playing his first Test in over two years, made a valuable Test-best 55 late on Monday.
It was a timely innings after Read's rival gloveman Geraint Jones, long regarded as the better batsman, had been dropped because of a lack of runs.
"It was a very important innings under pressure. I suppose he's felt he needs to show people he can bat at this level and he did a very good job by being positive," left-hander Strauss commented.
Looking ahead, the Middlesex batsman backed left-arm spinner Monty Panesar, who took three for 127 in 47.4 overs in the first innings, to play a key role.
Before this match, only one wicket had fallen to a frontline England spinner in 10 years of Test cricket at Headingley.
"There's probably a little bit more turn in the wicket now although it's not quick turn and the spinners have still got to work hard for their wickets," Strauss explained.
"But if Monty bowls like he did in the first innings, there's no reason why he can't get three or four wickets.
"I thought he bowled outstandingly. He was able to combine the two roles of keeping them quiet and being attacking at the same time.
"That was a particularly good effort on a wicket that didn't really suit spin bowling.
"Hopefully, it will suit a little bit more now and he can be one of our match-winners."
But Pakistan leg-spinner Danish Kaneria backed his side's batting line-up to come good against Panesar. "He will get turn but our batsmen are thinking positively and looking forward to getting the runs."