The Italy striker, who had previously netted once in 11 appearances for the Anfield club, came off the bench to equalise with four minutes remaining at Anfield on Tuesday night.
The goal helped Liverpool turn the tide and Dejan Lovren grabbed a stoppage-time winner to secure a 2-1 victory and a place in the quarter-finals.
Balotelli is now hoping his strike against Swansea will prompt a change of fortune, having cut an increasingly frustrated figure during a series of brooding performances since his 16 million pounds ($25.79 million) move from AC Milan in the close season.
"Finally!," the 24-year-old tweeted after Tuesday's game, relieved at finding the net for the first time since scoring his opening Liverpool goal in a home win against Bulgarians Ludogorets in the Champions League in September.
Assistant manager Colin Pascoe said Balotelli's Anfield intervention almost didn't happen because he tweaked his knee while warming up on the sidelines.
"He twisted his studs in the ground and was sent to see the physio to see if he was all right or not," Pascoe told reporters. "He felt something in his knee but he came on and his knee looked all right.
"I didn't know until the end of the game but, with the way he was moving about, I don't think there was much wrong with his knee.
"Mario is working hard and he got his just rewards by coming on and getting the goal -- it was great for him and something to build on."
Balotelli's Anfield future has been called into question in recent weeks and he was dropped from the starting XI on Tuesday after Liverpool were held at the weekend to a 0-0 home draw in the Premier League by Hull City.
In the dying moments of that match he failed to connect with a cross with the goal gaping and manager Brendan Rodgers subsequently decided to leave him out against Swansea.
Liverpool defender Kolo Toure, though, is expecting the League Cup goal to open the floodgates for his team mate.
"For strikers goals are like food," Toure told the Liverpool Echo newspaper. "Mario needs to feed himself by scoring goals. Now he's got that one he will do that now, definitely.
"Getting that goal will be fantastic for his confidence. He is a great player, he has just been lacking goals. Mario is my mate and I've tried to help him like (captain) Stevie (Gerrard), the manager and everyone else in the dressing room.
"We all know he's a top player. I always tell him 'you need to get out there and show you are one of the best players in the world'. He is one of the best. He has just been missing goals but they will come now," said Toure.