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Pakistan captain Misbah ul-Haq remained unbeaten on 83 at the close but England, the world's top-ranked team, made a good start to the match following their 10-wicket drubbing in the first test and Pakistan opener Taufeeq Umar admitted the tourists had the upper hand.
"I think they are in a better position because we lost a couple more wickets we were not expecting," Umar told reporters. "If we were at the same score at five (wickets) down, then I think we would have been in the better position. If we cross 300 runs that would be great."
Umar defended Pakistan's decision to bat first, saying that it meant England must bat last on what is likely to be an increasingly difficult wicket.
England's Monty Panesar, recalled in place of injured seamer Chris Tremlett for his first test appearance since 2009, said his team were happy with their start.
"Come the start of the day, we would have taken seven wickets," said Panesar. "You're going to get some chances taken, some chances dropped, but overall we're very pleased with the day."
The touring side looked like they might rue a hat-trick of missed catches as ul-Haq and Asad Shafiq put on a fifth-wicket stand of 100 to reach 203 for four but Swann and Broad struck in the final session to tip the balance in England's favour.
Pakistan, who play home matches in the Gulf region due to security problems in their country, started confidently. Openers Mohammad Hafeez and Umar added 50 as Broad and James Anderson struggled to make an impression with the new ball.
Captain Andrew Strauss then turned to spin duo Swann and Panesar, with England fielding a four-man attack including two slow bowlers for the first time since 2003, and the decision was soon vindicated.
In the 19th over, Swann bowled Umar for 16 with a straight delivery the batsmen foolishly left to clip his off stump, reducing Pakistan to 51 for one.
Panesar then dropped a stooping caught and bowled chance, but he made immediate amends, dismissing Hafeez for 31 with his next delivery, which squeezed between bat and pad to strike the leg stump as Pakistan reached 73 for two at lunch.
Broad returned to the attack after the interval and the all-rounder dismissed Younus Khan and Azhar Ali in quick succession, sending their off-stumps flying with searing deliveries.
Ul-Haq and Shafiq fought back, cheered on by a small crowd in the Sheikh Zayed stadium, an oasis of green in the industrial outskirts of the UAE capital.
Both batsmen had lucky escapes. Ul-Haq survived a fierce lbw appeal on nought, umpire Bruce Oxenford deciding the captain's bat hit the ball before it struck his pads, and he again escaped on 30 when Anderson put down a catch at slip off Panesar.
Alastair Cook at short-leg also failed to snaffle an edge from Shafiq before it hit the turf as the batsmen recorded his fifth test half-century.
Swann then trapped Shafiq lbw for 58 as he attempted a sweep shot, leaving Pakistan on 203 for five.
Strauss was found wanting as Anderson let rip with the second new ball, dropping an easy catch at slip after Adnan Akmal sliced an outside edge.
Broad then claimed his third wicket, Akmal falling for nine after being trapped lbw, and Abdur Rehman went for a duck as Swann snared him with a ball that turned sharply past the left-hander to hit off-stump.