Zamalek had the better chances and should have wrapped up the game, as they were quicker in everything and largely stifled the Chiefs scoring chances, until visiting goalkeeper Mohamed Sobhi spilled a routine Solomons cross into his own net in the 96th minute.
It leaves the AmaKhosi on a single point from their opening two games in the competition in their battle to qualify for the quarter-finals, while Zamalek have four and pool leaders Al Masry six.
Only the top two sides qualify for the knockout rounds.
It took under three minutes for Zamalek to take the lead. Chiefs goalkeeper Brandon Petersen was caught in no-and land as he attempted to come for a corner and missed the ball completely.
It was only half-cleared by Inacio Miguel to Seifeddine Jaziri, who curled his shot into the bottom right corner of the net.
Gaston Sirino almost hit back with a spectacular shot from the halfway line as he spotted Zamalek goalkeeper Sobhi slightly out of position and fired a powerful drive. It had the beating of the keeper but not the post and the visitors had a slice of good fortune in keeping their lead.
Chiefs lost both Sirino and defender Bradley Cross to injuries inside the opening 20 minutes, which did not help their cause.
Zamalek had the ball in the back of the net again inside 10 minutes but this time it was disallowed, perhaps a little fortuitously for Chiefs.
Miguel, whose massive error last time out in a 2-1 loss to Al Masry cost the AmaKhosi a point, left his back-header to Petersen short and Jaziri fired past the keeper.
But the officials felt the Tunisia international had pushed Miguel as they competed for the ball. If there was a touch it looked slight.
Chiefs had a piece of good fortune five minutes after the break as a melee in the box resulted in the ball trickling towards their goal. This time Miguel came up trumps and scooped it off the line with the Zamalek players closing in.
That proved crucial in keeping them in the hunt as Solomons provided a moment for Sobhi to forget when his tame cross inexplicably went through the hands of the keeper.
Chiefs will not be in action in the Confederation Cup until after the Africa Cup of Nations in Morocco when they go to Zambia side ZESCO United but do have two Betway Premiership games still to play in 2025, both away from home.
They are at bottoms side Chippa United on Wednesday and then go to TS Galaxy on December 7.