Stuart Broad took four wickets for 12 runs before the tourists declared on 258 for nine, leaving England chasing a highly unlikely 259 from 39 overs. Yet they took a calculated gamble by sending out Kevin Pietersen, whose 149 in the first-innings changed the complexion of the game, to open.
He fell in the fourth over, hooking Vernon Philander to mid-on and, while Matt Prior was also sent up the order to No.5, England effectively had to give up their pursuit once he was run out after a mix-up with Jonathan Trott. Trott and Ian Bell remained unbeaten until the close with the teams shaking hands on 130 for four after 33 overs.
"We felt it was worth having a go at it," Strauss said. "We sent in KP, who's obviously in outstanding form, to set things in action but once Matt Prior got out it was probably time to shut up shop. It was a bit of a tall chase in the first place but it was certainly worth having a go."
Pietersen, meanwhile, escalated his contractual stand-off with England by proclaiming next week's final Test at Lord's may be his last.
Pietersen held vexed negotiations with his employers at the England and Wales Cricket Board before his surprise retirement from all limited-overs international cricket was announced in June.
It seems the 32-year-old may be nearing a premature end to his Test career too, though.Pietersen followed his man-of-the-match performance at Headingley with a startling press conference in which he made it clear he may well not play beyond the final match of three against South Africa at Lord's next week.
He refused to set a deadline for a breakthrough in negotiations, or a settlement of "other issues" in the England dressing room.
Asked if the Lord's Test could be his last, the South Africa-born batsman admitted: "Anything's possible."