Errani was a runner-up in Dubai before, losing the 2013 final to Petra Kvitova.
"It's an unexpected title for me," Errani said. "You work to be ready for the matches, but you never know which days you can play better or worse. The only thing I know is that I was ready to suffer, to stay on the court if there were bad moments."
Strycova was trailing 6-0, 2-0 when the crowd cheered her as she came out to serve the third game. After Strycova finally won that game with a backhand volley, she raised her hands in a victory gesture.
"This is one of the days where you try everything and then nothing is working," Strycova said. "I tried everything and I couldn't put one ball in. I don't know why, what happened, but it's just sometimes how it is in tennis."
Errani became the first Italian to win the Dubai title on her fifth match point when Strycova netted the final shot.