Thousands of Palestinians and their sympathizers turned out at the 60,000-seat venue for the game against Australia, Palestine's first in front of fans since the start of the Israel-Hamas war.
Leicester center-back Souttar ducked and headed the ball past the outstretched hands of Palestine goalkeeper Rami Hamadi in the 18th minute off a Craig Goodwin corner to put Australia top of Group I.
The Australian team, before the start of the match, donated a portion of their fees towards humanitarian causes in Gaza. The Professional Footballers Australia said a percentage of player match fees would be directed towards Oxfam, via the PFA's Footballers' Trust.
Australia have won both their matches and are top of the group with six points.
The Socceroos won their opening match against Bangladesh 7-0, but Palestine proved a much tougher nut to crack. They had few chances, and the only other meaningful one came in the 64th minute when Hamadi got down quickly to deflect a Brandon Borrello shot.
Japan demolished Syria 5-0 at Prince Abdullah Al Faisal Stadium in Jeddah, to go top of Group B with two straight wins by the same margin.
Real Sociedad star Takefusa Kubo opened the floodgates in the 32nd minute. Ayase Ueda followed with a brace inside four minutes to make it 3-0 by the 40th minute.
Yukinari Sugawara made it 4-0 two minutes after the break and Mao Hosoya completed the scoreline in the 82nd minute.
In other matches in the Middle East, UAE defeated Bahrain 2-0 in Riffa's Bahrain National Stadium.
South Korea outclass China
Earlier skipper Son Heung-min scored a brace and set up the other as South Korea made it two victories from two with a 3-0 win in China.
Son silenced a sell-out crowd of more than 40,000 in Shenzhen with two goals in the first half, the first a penalty and the second a clever header from a corner just before half-time.
South Korea wrapped the game up in the dying minutes through a bullet header by Jung Seung-hyun -- from a Son free-kick -- and they top Group C with a perfect six points.
Jurgen Klinsmann's Korean side thumped Singapore 5-0 last week to begin their qualifying campaign in style and they were in much the same mood against an outclassed China.
The Koreans dominated and were ahead after 11 minutes when forward Hwang Hee-chan was brought down in the box and Tottenham Hotspur's Son duly stroked home the penalty.
It was all South Korea. Forward Cho Gue-sung headed just over the bar when unmarked from a corner and Son stung the palms of overworked goalkeeper Yan Junling.
Hwang In-beom's direct free-kick fizzed just past Yan's post midway through the half but China should have been level three minutes before the break with their first real chance.
South Korean full-back Lee Ki-je was dispossessed and Liu Binbin crossed for Tan Long, but the Chinese forward's first-time snap shot went narrowly wide.
They were to regret it on the stroke of half-time. Son leapt unmarked from a corner to direct his deft header back across the China goal and into the far corner.
South Korea, who reached the last 16 of the 2022 World Cup, should have gone 3-0 ahead soon after the restart but China defender Zhu Chenjie cleared off the line, before Jung put the game to bed.
Thailand are level on three points with China after winning 3-1 away at Singapore.
The top two from each of the nine groups in Asian qualifying for the World Cup will progress through to the final qualifying stage.
In other qualifiers in the region, substitute Mohanad Ali scored in the 97th minute for Iraq as they won 1-0 at Vietnam and top Group F with six points.
Iran surrendered a two-goal lead and had to settle for a point with a 2-2 draw at Uzbekistan.
North Korea thrashed Myanmar 6-1 away and Tajikistan won in Pakistan by the same scoreline.