England, at the fourth day’s close, were 258 for seven in their second innings after Strauss had scored 128.
Pakistan’s Test-record fourth innings total to win was the 315 for nine they achieved against Australia at Karachi in 1994/95. And the equivalent Lord’s record was West Indies’ 344 for one, requiring 342, set in 1984.
Leg-spinners Danish Kaneria (three for 73) and Shahid Afridi (one for 59) kept Pakistani hopes alive with tight bowling on a wearing pitch.
Left-handed opener Strauss, leading the side because of Andrew Flintoff’s ankle injury, became the third England player, after Archie MacLaren in 1897/98 and Allan Lamb in 1989/90, and first at home to score a century in his debut Test as England captain.
His ninth Test century was also his third at Lord’s, after he scored 112 here on his debut against New Zealand in May 2004 and 137 against the West Indies two months later.
“It was a tricky situation as we were losing wickets at important times and we couldn’t push on,” said Strauss. “We needed someone to stick around and fortunately I was able to do that.
“I’ve had a frustrating time this year; getting 20s and 30s isn’t good enough for Test cricket. It was a case of overcoming that, the wicket here was flat and it was nice to get to three figures.”
Strauss will sleep on a decision whether or not to declare first thing today, the final day of the match.
“The wicket is flat so we have to take that into consideration. We’ll have to bowl well. The ball bounced a little for their spinners today. Hopefully (off-spinner) Monty Panesar can get that and be a threat.”
At stumps Liam Plunkett was five not out and Matthew Hoggard unbeaten on nought.
England began the final session on 154 for four after Kevin Pietersen and all-rounder Paul Collingwood fell to Afridi and Kaneria respectively.
Strauss was one away from his century when Ian Bell was run out for 28 by Pakistan captain Inzamam-ul-Haq’s direct hit from mid-wicket after Strauss hesitated after setting off. However, the 29-year-old got the run he wanted when a single off Afridi took him to a 168-ball century with 11 fours.