Danish 18-year-old Højgaard became the third youngest winner in European Tour history when he won the AfrAsia Bank Mauritius Open earlier this season and a second round 68 put him on top of the leaderboard once again at nine under.
Scot Gallacher - whose son and caddie Jack was born nine days before Højgaard - has four European Tour wins in his 45 years and he went one better with a 67 to share the summit at Al Mouj Golf.
Højgaard made a flying start from the tenth, eagling the par five 12th to leapfrog overnight leader Guido Migliozzi before making birdies on the 14th and 15th to get to nine under.
Bogeys on the 17th and 18th stalled his progress and he was in a share of the lead with Gallacher, who birdied the fifth seventh and eighth to turn in 33.
Gallacher's playing partner Samooja also turned in 33 as he recovered from an opening bogey with gains on the second, third, sixth and eighth.
Højgaard holed a 20 footer on the first to get to eight under but he soon had company as Samooja birdied the tenth and 11th and then holed a 15 foot putt for eagle on the next.
Gallacher got up and down from the sand on the 12th to make it a three way tie and a long putt on the next put him ahead alone before Samooja followed him in.
Højgaard three putted the third but picked the shot back up from 18 feet on the fifth, before a two putt birdie on the par five seventh had him back in a share.
Samooja found water on the 15th to surrender a triple bogey but got a shot back on the par five next and holed a long double breaker on the last to get back within one.
McEvoy - playing alongside Gallacher and Samooja - birdied the third and ninth and then made a hat-trick of gains from the 12th before dropping a shot on the last.
Rock matched Samooja's 65 with birdies on the first, second, ninth, 11th, 12th, 14th and last.
Paraguayan Fabrizio Zanotti double bogeyed the last in a 70 that left him at five under alongside Italy's Lorenzo Gagli - who has started 69-70 after his reinstatement into the field following a negative test for coronavirus.