South Africa can now replace England at the top of the test rankings with a 3-0 win over New Zealand in March.
With the ball turning again it was always a difficult task for England's batsmen, who have been unable to play the Pakistani spinners, on a wearing fourth-day pitch at Dubai Stadium.
Pakistan won the first test here by 10 wickets and the second by 72 runs in Abu Dhabi.
It was England's seventh series whitewash, their first at the hands of Pakistan. So dominating have been Pakistan's spinners that Ajmal finished the series with 24 wickets and Abdur Rehman 19.
An elated captain Misbah-ul Haq praised his team.
"It's a wonderful team effort," said Misbah, who has won nine of 15 tests as captain. "It's a big win against a big team, achieved through hard work."
England captain Andrew Strauss said the lack of run-making had left him disappointed.
"It's a bit of a surprise as well as disappointment because we did not put scores on the board, and we must give credit to Pakistan," said Strauss.
The teams will now play four one-day and three T20 internationals.
- AAP