PSV had a goal disallowed, missed a penalty and had two further strong shouts for a spot-kick waved away by the officials as last year's runners-up Atletico got their campaign off to a fortuitous start.
The Dutch champions thought they had taken the lead inside the opening six minutes when captain Luuk de Jong headed home from close range. Referee Martin Atkinson, however, ruled that there was a push in the build-up by PSV defender Hector Moreno.
Lively PSV forward Luciano Narsingh wanted a penalty for a shove in the box midway through the first half and looked to have a case.
Yet it was Atletico who took the lead on 43 minutes when Saul volleyed home at the second attempt as PSV failed to clear his initial shot following a corner. As the ball rebounded to him on the edge of the box, he skilfully steered his effort into the goal.
PSV had much of the ball in the second period but should have fallen further behind when Kevin Gameiro found himself in space in the box, but the Atletico forward fired wildly over the bar.
The home side were incensed not to get another penalty with 15 minutes remaining, claiming a handball by Diego Godin, but did have a golden chance to rescue a point late on.
Uruguayan forward Gaston Pereiro, however, could only direct his free header straight at a grateful Oblak.