Ruben Sobrino had given last season's beaten finalists the lead shortly after the hour mark, but Goncalo Guedes quickly restored parity and Rodrigo completed the comeback eight minutes from time after Alaves had seen Adrian Dieguez pick up a second yellow card.
The match pitted third from top in La Liga against fourth from bottom, but it was Alaves who applied the early pressure and they could have been two up inside five minutes.
Sobrino first managed to work space to shoot from inside the box only to fire just wide, before Hernan Perez rattled the post with an effort moments later.
Valencia soon settled into the game, though, and they had their first meaningful sight of goal after 16 minutes when Guedes drilled an effort wide from the edge of the box.
It was Alaves who looked most like breaking the deadlock before half time, though, and Perez came close again when only a fine stop from Jaume Domenech denied him shortly after the half-hour mark.
Domenech was back in action again two minutes later when John Guidetti lined up a free kick and fired it on target, but the Valencia keeper got across to make the save.
The hosts fought back in the second half and were the first to threaten on the hour mark when a ball into the box found Luciano Vietto, only for the striker to plant his header well over the crossbar when he should have done better.
Valencia were soon back on the attack and came within a whisker of opening the scoring shortly afterwards when Rodrigo's close-range effort skimmed the post on its way behind.
Within seconds Alaves had the ball in the back of the net at the other end of the pitch, though, with Sobrino collecting Munir El Haddadi's pass before firing a fine long-range effort into the top corner.
The visitors' lead lasted only seven minutes before Valencia were level again, with goalkeeper Antonio Sivera being deceived by the movement on the ball from Guedes's shot as it flew into the back of the net from outside the area.
Things went from bad to worse for Alaves when they were reduced to 10 men just four minutes later, with Dieguez picking up a second yellow card to receive his marching orders.
It took only five minutes for Valencia to make the most of their numerical advantage as Rodrigo latched on to a pass inside the area before calmly stroking his finish past the keeper with eight minutes remaining.
There was no way back for Alaves after that as Valencia extended their unbeaten run to five games, although they only take a slender advantage into next week's second leg at the Estadio de Mendizorroza.
VALENCIA (4-4-2): Domenech; Montoya, Garay, Gabriel, Gaya; Pereira (Rodrigo, 58'), Parejo, Kondogbia, Guedes; Zaza, Vietto (Mina, 71')
ALAVES (4-4-2): Sivera; Martin, Maripan, Alexis, Dieguez; Perez (Gomez, 76'), Torres, Pina, Wakaso (Pedraza, 68'); Guidetti (Munir, 62'), Sobrino