Former world number one Wozniacki made short work of Bosnian qualifier Mervana Jugic-Salkic with a 6-1 6-2 win in a little over an hour of play.
"It's tough to play your first match at any tournament and tough to play an opponent you haven't played before, but I just tried to focus on my game," Wozniacki said after the match.
"I felt like I served well and returned well during the match, so I was happy with how things went today."
The win puts the Dane back into the top 10.
Later in the day, Ivanovic recorded a more impressive win by seeing off 26th-ranked Austrian Tamira Paszek by the same scoreline with two breaks in each set.
''I actually expected a very tough match. We had some battles in the past, but I really started well and I was aggressive,'' Ivanovic, another former world number one, said.
''I felt like I was doing like lot of damage with my forehand, so I tried to keep that game plan.'
'Qatar Open first round results
10-Caroline Wozniacki (Denmark) beat Mervana Jugic-Salkic (Bosnia and Herzegovina) 6-1 6-2
13-Ana Ivanovic (Serbia) beat Tamira Paszek (Austria) 6-1 6-2
Caroline Garcia (France) beat Fatma Al Nabhani (Oman) 6-2 6-3
Daria Gavrilova (Russia) beat Anabel Medina Garrigues (Spain) 4-6 6-3 6-3
Anastasia Rodionova (Australia) beat Zheng Jie (China) 6-2 6-3
Mona Barthel (Germany) beat Yulia Putintseva (Kazakhstan) 6-4 6-2
Simona Halep (Romania) beat Olga Govortsova (Belarus) 6-1 6-0
Svetlana Kuznetsova (Russia) beat Bethanie Mattek-Sands (US) 7-6(1) 6-4