Diego Simeone named a surprising line-up, with all three of his side's star attackers - Antoine Griezmann, Diego Costa and Alvaro Morata - starting in attack.
But it was Saul who was involved in the side's opening attacks, first missing a gilt-edged chance only three minutes in before having the chance to make amends with an identical opportunity eight minutes later. Arriving on the left-hand side of the area, the Spaniard made no mistake in driving a low shot into the far corner of the net.
Then the Atletico forwards did get in on the act. Diego Costa, who has recently returned from injury, picked the ball up with his back to goal. He took one touch to control and turn before going for goal with his second. Despite being 25 yards out, his bending effort was inch-perfect and grazed the post on its way into the Alaves net.
The hosts reponded well from their disastrous opening quarter of an hour, and forced Atletico goalkeeper Jan Oblak into a couple of good saves.
Costa was replaced at half-time, sparking fresh injury concerns, but the team continued as before, with Alvaro Morata grabbing the third on the hour mark. Alaves were throwing too many men forward, and were exposed brutally. Morata found himself with half the pitch to run into as he broke away from the home defence, eventually reaching the penalty area and lobbing the onrushing Alaves goalkeeper Fernando Pacheco.
With Costa and Morata both now on the scoresheet, Griezmann was the only one of Atletico's new-look attacking trio not to score. He had his chances, and saw a lobbed attempt hit the post with 20 minutes to go. But it was an ultimately frustrating evening for the Frenchman, and he was eventually replaced by Andrea Correa.
Thomas Partey, Atletico's right-back turned central-midfielder, struck the final goal of the game. Receiving the ball on the edge of the area, he bent the ball perfectly into the top corner of the net, giving Pacheco no chance. It was a goal that resembled Costa's first half strike, and one that was heartily applauded by watching manager Diego Simeone.
The win moves Atletico back to within 10 points of league leaders Barcelona and means they now lead their city rivals Real by five points, albeit having played one game more.