In what was Andoni Iraola's first home game in charge of the Reds, the Sweden striker struck in the 16th minute, latching onto a Ryan Gravenberch assist for a clinical finish, before combining with Florian Wirtz for a scrappy second on the half-hour mark that put Liverpool 2-0 up.
Monaco fought back through an Aleksandr Golovin penalty on the stroke of half-time, before Mika Biereth's rebounded finish and a late Paris Brunner header completed the turnaround.
Isak, making his second appearance of the summer programme after a lengthy World Cup campaign with Sweden, said simply being back out at Anfield had been a welcome feeling.
"It was good. Really nice to be back at home, back in front of the fans and get some more minutes into the legs," he said. "So, that felt good."
There was some confusion over who exactly got the final touch for Liverpool's second goal, with Isak unable to say for certain whether it was his effort or Wirtz's that crossed the line.
"I think we agreed, me and Flo, that we both got a touch on the ball," he said. "But obviously I don't know who got the first one or the last one. It felt like I was on the ball. I don't really know."
On his own fitness levels as pre-season progresses, Isak said he was continuing to build towards peak sharpness ahead of the new campaign.
"I feel good, I feel good. Every game hopefully should take me to a better fitness level, so that's what I'm working towards," he said. "I think today felt better than the last game and hopefully the next game feels better than today. That's what pre-season is for - building - and that's what we have to keep doing."
The forward also gave an early verdict on life under Iraola, who replaced Arne Slot as Liverpool head coach over the summer after three successful seasons at Bournemouth.
"Really good. I feel like the spirit is good in the group and we're all working hard to make things work," Isak said. "We're going to make sure that we're ready for the start."
Liverpool's next test comes as their pre-season schedule continues ahead of the Premier League opener away to Newcastle United later this month, a fixture that will mark Iraola's competitive bow at the club after succeeding Arne Slot at Anfield in the summer.