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 first day at the Dubai International Cricket Stadium.
England battled back with some important wickets but Adnan Akmal, unbeaten on 24 at stumps, will hope to stretch the lead with the tailenders when he returns on Thursday.
"Overall we are very happy," Hafeez told Sky Sports. "We're happy with the effort of the batsmen because England's seamers really bowled well.
"We're in a good position because the conditions at the moment have a little bit of turn, as we saw when Graeme Swann got some, so I think we're in a good position and can dominate a bit from here.
"The conditions are really tough to score runs in because the outfield is not very fast."
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 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-colour, accounted for Asad Shafiq (16) but Misbah played with characteristic caution to complete his 15th test fifty and found an able ally in Akmal.
Despite the deficit, Broad felt England had were back in contention.
"We set a target today of going under three an over and didn't worry too much about the wickets because we knew if we built the pressure that way, they would come," he told Sky Sports.
"I think we really earned those wickets late on in the day today...more importantly on Thursday morning we've got to come out and finish the tail off."
Pakistan are hosting the three-match series in the Gulf due to security concerns in their own country.
