Safarova, the world number 17 and Czech number two, needed an hour and 41 minutes to sink world number 12 Ivanovic on the hardcourt of Prague's O2 Arena.
Ivanovic, a former world number one, never found the pace to match her left-handed rival, making 32 unforced errors against Safarova's 18.
Serbian number one Ivanovic was broken twice in both sets, letting Safarova improve her head-to-head winning streak to four victories.
"The key was to shake off the nervous feeling. I was improving through the match," Safarova said just after the game.
The turning point she added came "in the first set when I broke her and took a 5-2 lead.".
In the second rubber on Saturday, Czech number one Petra Kvitova, who is recovering from a cold that forced her to pull out of the WTA Championship last week, will face Serbia's number two Jelena Jankovic.