The 32-year-old beat the Croatian 6-3, 4-6, 6-0 to set up a match against Marcos Baghdatis in the Dubai Duty Free Tennis Stadium yesterday.
Monfils and Svitolina, 24, confirmed they are in a relationship last month during the Australian Open.
They even set up a joint Instagram account with the couple posting cute pics and videos from their training sessions.
Ukrainian Svitolina is a two-time champion in the Emirates but lost in the semi-final last week.
“That’s the beauty of the relationship”
But she was on hand to cheer on her man in the stadium yesterday.
Monfils, who won in Rotterdam earlier this month, said Svitolina was very intense in the way she approaches her tennis.
He told reporters: “I admire what she’s doing, how she works, the mentality she has. It’s incredible.
“But I always say but not for me, not for me. She’s too serious for me. It’s her way.
“It’s her way to be where she is. Even to become better, you know.”
But despite this, Monfils did say her personality means the relationship works.
He continued: “Me, the only motivation that I will say that we have is to make the other proud.
“I love when she win. I’m very proud of her. I think same for her.
“For myself, I’m serious on my way, which is normal. It’s not different.
“I put a lot of work with my coach, a lot of work with myself to be back. Definitely is a bit different than her.
“At the end we try to be at the top with different ways, different culture. That’s the beauty of the relationship.”
Monfils is ranked world number 23 and reached a high of 6th in 2016.
Svitolina is number seven after an impressive run to the quarter-finals at the Australian Open in January.
She will be hoping to go further at a grand slam for the first time at the French Open which starts in late May.
She has also revealed she has a tattoo on her thigh of a big cat.
Svitolina previously spoke about it, telling reporters it means carpe diem, or to make the most of the present.
She said: “It’s very personal, actually.
“I know that you can see parts of it, but, yeah, it’s quite personal.
“You know, it’s like my way.”
The tattoo does have a “special meaning” for her – but Svitolina has remained tight-lipped on what that could be.