Vitolo's successful spot-kick after he had been fouled in the area by Ales Mertelj came just 12 minutes after he had struck a post with an earlier penalty.
Maribor played the entire second half with 10 men following Ales Mejac's dismissal for two quickfire yellow cards just before the break.
The win means the Greek side will go through if they beat Tottenham in their final Group J match at White Hart Lane next month.
With both sides needing a win to stand any chance of going through, nerves were evident in the opening exchanges before Ibrahim Sissoko had the first chance in the 11th minute for the home side when he blazed over the bar.
Toche headed just over in the 16th minute from a cross by Quincy Owusu-Abeyie as the home side pressed, then Jose Carlos Zeca missed with a header from a cross by Nikos Spyropoulos.
Maribor had their first chance just before the half hour when Robert Beric's shot from 20 yards was caught by Panathinaikos goalkeeper Orestis Karnezis.
Toche forced Maribor keeper Jasmin Handanovic to save with his feet from his shot on 42 minutes before the same player brought another save out of the keeper as the home side finished the first half on top.
And Maribor's hopes faded on the stroke of half-time when Mejac was dismissed for a second bookable offence after a deliberate handball.
The home side looked to press home their advantage early in the second period with Giorgos Seitaridis firing just wide, but Maribor responded with a good effort from Mertelj.
And the home side's frustration grew in the 52nd minute when Arghus handled in the box, but Vitolo struck his first penalty of the night against Handanovic's left upright.
Spyropoulos drilled a shot over the bar from long range and Zeca saw a header in the area blocked by Handanovic before Vitolo got his second chance from the spot and this time shot low into the bottom left corner.
Handanovic was increasingly busy in the dying minutes, saving well from Charis Mavrias and also denying Antonis Petropoulos, before Beric missed a fine chance to equalise in injury time when his shot was parried by Karnezis.