Having found the back of the net in Australia's 7-0 thrashing of Bangladesh in Melbourne last Thursday, the towering defender again scored in neutral Kuwait to ensure the Socceroos started their 2026 World Cup qualifying campaign with back-to-back wins.
Souttar, who is out of selection favour with his English Championship club Leicester, was also commanding in defence in a match that was a lot tougher for Australia than perhaps many expected.
Socceroos captain and goalkeeper Mat Ryan was also crucial in the win, making a great save in the dying stages of the first half when attacker Tamer Seyam seemed certain to score after the Australians failed to deal with a Palestine corner.
Souttar had earlier given the Socceroos the lead when he headed home an 18th-minute Craig Goodwin corner to score his 10th goal for Australia.
Harry Souttar (right) heads the Socceroos into the lead against Palestine
Australian players celebrate after Souttar's goal, which came after he also scored in the big World Cup qualifying win over Bangladesh
The pair had also combined against Bangladesh when Souttar scored from a Goodwin free-kick.
But while that game opened up the floodgates at AAMI Park, it was a different story at the Jaber al-Ahmad International Stadium where the Australians toiled for long periods of the contest.
Socceroos coach Graham Arnold made four changes to the team that started against Bangladesh.
Three of those were in defence, with Ryan Strain, Aziz Behich and Kye Rowles coming in for Lewis Miller, Jordan Bos and Cameron Burgess.
The other change was in attack where star winger Martin Boyle, who wasn't risked against Bangladesh because of knee swelling, returned at the expense of Western Sydney Wanderers star Brandon Borrello.
Supporters wave Palestinian flags prior to the match
Palestine was well represented in Kuwait, with their fans far outnumbering Aussie supporters
However, Strain only lasted 20 minutes before injuring his groin and being replaced by Miller.
Borrello was among those injected into the game during the second half, with the Western Sydney Wanderers forward forcing a good save out of Palestine goalkeeper Rami Hamadeh in the 64th minute.
From the subsequent corner, the Palestinians were saved by the woodwork when a header from Bos, who was also one of the second-half substitutes, hit the crossbar.
Souttar admitted the Socceroos could 'play a whole lot better'.
'I don't think we were best pleased with our performance,' the giant centre-back told Network 10.
'It's a great lesson for us as a team, for a couple of the new guys coming into the squad, about playing games away in Asia.
'If you want to go through and qualify (for the World Cup), these are the games you've got to win.'