In a bad-tempered clash which saw both teams finish the game with 10 men, Piti claimed the winner just after the half-hour mark.
Granada's Dani Benitez was shown a straight red card with 10 minutes to go and Antonio Amaya picked up a second yellow card in the dying minutes in a match which saw referee Jose Antonio Teixeira Vitienes show a total of nine yellow cards as well as the two reds.
Granada had gone into the game 10 points above their bottom-placed rivals but only one place clear of the relegation spots following a 1-0 defeat to Espanyol last time out.
But Betis had themselves suffered a 5-0 mauling to Valencia and Gabriel Calderon's side failed to bounce back as Piti secured all three points for coach Lucas Alcaraz.
Granada started the game well and forced Antonio Adan into three saves in the first two minutes from Yacine Brahimi, Youssef El Arabi and Fran Rico.
Ruben Castro had Betis' first effort after seven minutes but his shot was comfortable for Roberto Fernandez.
The game was 26 minutes old when Amaya picked up his first booking for a foul on Brahimi.
But from the free-kick which was played into the area by Piti, El Arabi shot weakly from close range straight at Adan.
Four minutes later Granada got the decisive goal as Piti finished after a long ball forward by Tiago Ilori.
In a rare period of dominance by the away side Jose Nono saw his shot blocked by Jeison Murillo before Ruben Castro picked out keeper Fernandez with the next effort.
Early in the second half Betis nearly took the lead but for a fine save by Fernandez.
Fran Rico was penalised for fouling Ruben Castro and from the free-kick Joan Verdu picked out Jorge Molina Vidal but Fernandez somehow parried his header away.
In a match which continued to be littered with fouls and chances were few and far between Granada were reduced to 10 men with 10 minutes to go.
Dani Benitez was shown a straight red card for his tackle on Jose Nono.
But Real Betis could not make their man advantage tell as Granada saw out the remaining time to claim the win.
Things got worse for visitors in injury time as Amaya was sent off for his second bookable offence.