Russia's Voskoboeva raced through the first set in Uzbekistan and the seventh seed's dominance saw her clinch a convincing 6-1 lead.
But world number 58 Jovanovski regrouped and levelled the match after taking the second set 6-4 before taking the decider on a tie-break - the Serbian eventually advancing to the final four with a 1-6 6-4 7-6 (7/5) win.
She will challenge Maria-Teresa Torro-Flor for a place in the final after the Spaniard took little time in overcoming third seed Yvonne Meusburger, winning 6-3 6-0 in just 51 minutes.
Olga Govortsova of Belarus will face Mandy Minella in the other semi-final after both players secured straight-sets quarter-final victories.
Luxembourg's Minella beat Nastassja Burnett of Italy 7-6 (6/4) 7-5 to set up a meeting with Govortsova, who saw off fifth seed Alexandra Cadantu 6-3 6-2.