Jon Rahm has taken the outright lead at the Abu Dhabi Championship following the third round of play.
Hatton and Laporta both carded a 67, as did McIlroy, who goes into the final round in fourth place on 16 under.
Rahm, who said recently that he does not know what 2027 holds after quitting the LIV tour, is aiming for a first solo tournament triumph since winning the Masters in 2023.
The 31-year-old Spaniard shared the overnight lead with Italy's Francesco Laporta and fellow former LIV player Hatton, but moved clear of them both with a six-under-par 66 at Yas Links on Saturday.
Hatton is looking forward to going head-to-head again with Rahm after playing alongside the two-time major champion in Saturday's final group.
Reigning Masters champion McIlroy remains in hot pursuit, however, after bouncing back in spectacular fashion since being given a two-shot penalty in the opening round for improving his lie before taking a chip shot.
The six-time major winner hit 11 birdies in a second-round 63 and another eight in his third round, but a double bogey six at the par-four 10th - and another dropped shot at the 17th - left McIlroy two shots off the lead.
He reclaimed the outright lead on the 15th with a superb, curling 20-foot birdie putt and came close to extending his advantage at the last, just coming up short with another birdie chance as he finished without a single dropped shot.
Laporta also produced a bogey-free round to keep pace with the field's big hitters as the 36-year-old, who shot 10 under par to claim a first-round lead, bids for a first title on the DP World Tour.
Elsewhere, Australian Adam Scott remained bogey-free for the tournament after three rounds and moved up to fifth place on 15 under with a 66.
And Englishman Matthew Jordan is a shot further back, alongside Spain's David Puig, after a third-round 69.