Dyson - twice a winner at Kennemer and once at Hilversum - closed the gap to one shot after covering the back nine in 31 and picking up shots on the first and second.
However, Jiménez - himself a winner of the tournament back in 1994 - responded superbly by holing from ten feet for a birdie on the par three third and six feet on the fourth to improve to nine under par and move three shots clear.
Fisher had picked up a birdie on the 18th to join Dyson in second place on six under, but Allenby had slumped seven shots off the pace after running up a triple-bogey seven on the first.
Dyson, whose victories at Kennemer both came in play-offs, was not about to let Jiménez establish a sizeable lead and birdied the sixth and seventh from close range, almost driving the green on the short sixth and then hitting an excellent approach to the par five seventh.
That took him to eight under par, one behind Jiménez and two clear of fellow Englishman Fisher, who remained six under.