Chelsea have only dropped points in four games this season, with three of those coming in March.
After draws against Brighton and West Ham in the WSL and a Champions League quarter-final first leg defeat by City last month, Bompastor said she wanted to see the best version of her players on their return from the international break.
The Blues were far from their brilliant best but, like so many times this season, dug deep to get the job done when it mattered.
France international Baltimore was their bright spark and creative outlet and enjoyed a fascinating tactical battle with Liverpool captain Taylor Hinds down the left hand side.
It was Baltimore's tricky footwork in the six-yard box that kept the ball alive before Cuthbert lobbed Laws for Chelsea's first goal, and the France defender kept her composure to put the ball on a plate for Beever-Jones to head in the decisive winner.
With only eight days to prepare for the trip to Barcelona, Chelsea desperately wanted to avoid extra time, and Beever-Jones made amends for her earlier missed chances to deliver the perfect outcome for Bompastor's quadruple-chasing Blues.
"It was a dramatic game, a lot of emotions," Bompastor said after the game. "When we conceded we stuck to our principles, stayed strong and tried to score which we did.
"I told my players we need to stick with the game plan and that was the right thing to do today. Keep the belief and try until the end. It's important to stay patient and have belief."