The most successful club side in Iraq stunned the Saudis at the rebuilt Khalifa International Stadium, one of the venues for the 2022 World Cup in Qatar.
The victory moved them up to four points which means they require just one point from their next match against Esteghlal of Iran to progress to the knockout stage from Group A.
Al Ahli had become the first team to make the cut on Monday, their cause helped by the fact that the UAE's Al Wahda were considered withdrawn from the tournament after several of their players tested positive for Covid-19.
In 1971, they arrived back to a rousing welcome in Baghdad after reaching the Asian Champion Club Tournament's final and became part of Arab folklore but thereafter failed to make much of an impression when the competition was rebranded as the Asian Club Championship in 1985 and again as the Asian Champions League in 2002.
On Thursday, it was Al Shorta who opened their account first as Saad Natiq produced a powerful header in the 14th minute off a fine Ali Fayez cross to completely fox the Al Ahli goalkeeper Mohamed al-Owais.
Both teams enjoyed short spells of domination and Al Ahli got the equaliser in the 56th minute with their sustained pressure paying off.
Mohamed al-Majhad collected a measured pass from Marko Marin, got past the Al Shorta defence and fired the ball low beyond goalkeeper Ahmed Basil in the 56th minute.
But it didn't take much time for Al Shorta to regain composure and sure enough they went ahead again in the 65th minute with Mazin Fayyadh making the most of a low cross from Kudhur Ali on the right flank.
In Group B on Thursday, substitute Pedro Conde struck in the 83rd minute to help the UAE's Shabab Al Ahli beat Iran's Shahr Khodro 1-0.
Shahr Khodro had lost to Shabab by a similar margin on Monday and with Thursday's defeat stand eliminated from the tournament with no points from four matches.
Also in the pool, defending champions Al Hilal of Saudi Arabia and Uzbek giants Pakhtakor played out a goalless draw at the Al Janoub Stadium.
Al Hilal who had beaten Pakhtakor 2-1 on Monday are on 10 points at the top of the table while Pakhtakor are second with seven and Shabab Al Ahli third on six.