Openers Hafeez (88) and Umar (58) shared a 114-run stand and captain Misbah-ul-Haq struck a patient 52 as Pakistan reached 288 for seven after bowling England out for 192 on the opening day at the Dubai International Cricket Stadium.
Adnan Akmal was unbeaten on 24 at stumps and will have the tailenders for company when he returns on Thursday.
Resuming on 42 for no loss, the right-left combination of Hafeez and Umar thrived on a placid track, helping themselves to easy boundaries on offer.
Umar hit Chris Tremlett for two boundaries in the same over on his way to a 13th half century and Hafeez took a single off the same bowler to score his seventh fifty.
Desperate for a breakthrough, England captain Andrew Strauss brought Stuart Broad back into the attack and the change paid off when the lanky bowler, from around the wicket, pegged back Umar's off-stump.
Broad returned to remove Azhar Ali (one), who poked outside off-stump to depart caught behind.
Hafeez looked good for his fifth test century but paid the price for playing a premeditated sweep off Graeme Swann to completely miss the line.
Even reviewing the leg before decision could not save him and Hafeez departed after a measured 164-ball knock that included 11 fours and a six.
Younus Khan (37) appeared to have settled in for a long stay but another clever bowling change by Strauss sent him back.
With the former Pakistan skipper looking comfortable against pace and spin, Strauss tossed the ball to occasional bowler Jonathan Trott and the medium pacer trapped Younus leg before, only his third test victim.
James Anderson, otherwise off-color, accounted for Asad Shafiq (16) but Misbah played with characteristic caution to complete his 15th test fifty and found an able ally in Akmal.
Pakistan are hosting the three-match series in the Gulf due to security concerns in their own country.
