Ms Monaghan, from Holywood, was at the zoo with her two children Grace, eight, Leo, six, her partner Dean McFaul and his four-year-old nieces Summer and Willow.
They filmed the entire escape from start to finish, and Ms Monaghan said it was a day she would “never forget”.
She said they “could not believe it” when the “smart” chimpanzees started to climb out of the enclosure, and when they went to take a closer look, they ended up “a foot” away from one of them.
“I was petrified, obviously, having the kids and I tried not to show fear but inside I was a bit like what happens if it attacks us or tries to take the kids or runs over,” she told BBC News NI.
“But we just had to stay calm.
“It may have been a different story if it had been aggressive but it absolutely wasn’t. It made us feel at ease. We just walked past it and it was absolutely grand.”
Mrs Baxter, from Larne, said when the chimpanzee appeared before them, her youngest child shouted at it.
“I think she scared it and it did sort of make its way back up the hill,” she said.
“But there were four of them that we could see were out. There was one on the path and there were three of them sitting on the wall.
“We were a bit shocked, obviously, being approached by this big chimpanzee. The kids were shocked.
“I suppose now it’s easy to think it was funny, but it was quite dangerous.”
Belfast City Council, which runs the zoo, said one chimpanzee “briefly” left its enclosure.
“Zookeepers were present as the chimpanzee quickly returned from an adjacent wall to the rest of the group inside the enclosure,” a spokeswoman said.
The zoo’s Alan Cairns said: “We think what has happened is that the trees in their enclosure have been weakened by the storms and so they’ve been able to break them and use them as a ladder to get out.
He said the zoo’s chimps were “quite cowardly” so went back into their enclosure themselves during the incident.
“They’re intelligent primates and know they’re not supposed to be out of their enclosure, so got back in themselves,” he said.
“We like things to be natural in their enclosure, to have trees in it, but we will review it.
“We may have to remove the trees or make them a smaller level, although we don’t want to do that.”
The chimpanzees were locked into their inner enclosure after the great escape.
Chimpanzees are one of four types of “great ape” – the others being bonobos, gorillas, and orangutans
Humans and chimpanzees share 95% to 98% of the same DNA
Chimpanzees walk on all fours and have longer arms than legs
Chimpanzees sometimes hunt and eat small mammals such as bushbuck or monkeys
They also eat fruit, nuts, seeds, blossoms, leaves, and many kinds of insects
A full-grown chimpanzee has five or six times the strength of a human being