The tournament, which resumed after almost seven months following the outbreak of the new coronavirus pandemic, is being played in the Qatari capital where spectators are barred and players and officials subject to regular testing under strict health protocols.
Two-times runners-up Al Ahli progressed to the last 16 after the UAE's Al Wahda were considered withdrawn from Group A as they failed to travel to Qatar following several positive tests among the squad for Covid-19.
That meant the Saudi side had to secure only three points to guarantee a top-two finish in the three-team group, and Marin's 87th-minute strike from close following a pass from Abdulrahman Ghareeb ensured just that at the Khalifa International Stadium.
In a fast-paced match both teams missed close chances with the goalkeepers called into play several times.
Al Shorta were reduced to 10 men seconds before the first half ended with Ali Mhawi earning his second yellow card, but that didn't seem to matter much as the Iraqis still managed to create pressure for their rivals..
However, Al Ahli gained control towards the final 20 minutes and following an exchange of passes Marin produced a calm finish from six yards to help his team earn three points.
Marin, who was named player of the match, was delighted with his team's win.
"Of course, I am very happy to be named player of the match, but I have many other reasons to be happy," said Marin, who played in the 2010 World Cup for Germany.
"I am happy to play an official game after a long time on the sidelines. I am happy that I am fit again and fully recovered after weeks of absence from training.
"It was a difficult injury and I am happy to start the competition with a win against a strong team like Al Shorta. It was a great performance and we are happy to get the win," he added.
- Terrific solo goal -
In another early match, substitute Harib Abdallah scored a brilliant solo goal as Shabab Al Ahli of the UAE pipped Iran's Shahr Khodro 1-0 to open their points tally in Group B.
Both sides were under pressure having lost their two opening matches but Abdallah produced a dazzling run down the right flank getting past several Shahr Khodro players before scoring in the 75th minute.
Shabab's Spanish coach Gerard Zaragoza was pleased with his side's performance.
"I would like to congratulate my players who played really well in our first competitive match in six months. They fought hard and earned the three points," said Zaragoza.
"It was not easy for us to play after such a long break, a lot of work was required to prepare a team that can show the world we are ready.
"We trained and prepared in extremely hot weather in UAE, but today we played in an air-conditioned stadium which made things easier for us, especially in transitions between defence and attack."
In a late match, defending Asian champions Al Hilal of Saudi Arabia edged past Uzbek giants Pakhtakor 2-1.
Italian Sebastian Giovinco put Al Hial ahead in first-half added time, but Pakhtakor's Swiss-born striker Erin Derdiyok restored parity in the 70th minute after he was left unmarked deep inside the penalty area.
The match appeared headed for a draw but Saudi midfielder Hattan Bahebri sealed Al Hilal's third win in as many matches with a powerful drive in the seventh minute of second-half stoppage time.