A double from Abdallah Sima, and goals from Ridvan and Ryan Jack set up a last four tie with Hearts at Hampden in November. The Gers’ boss was happy with the control his side showed tonight at Ibrox as they kept their fourth clean sheet in a row.
Speaking to RangersTV at full-time, he said: “I am really happy with another clean sheet, I don't think we gave up a shot on our goal which in any game of football is a really pleasing thing.
“As a team I felt in the first half we had a lot of controlled possession, and we were trying to make Livingston come out or play through or around them. That is how we scored the first goal, and it was a fantastic goal from Abdallah Sima.
“I am delighted with him the last few games, he had a big contribution against Betis, he came off the bench at the weekend because we wanted to keep him fresh for tonight and he has rewarded us with two goals and an excellent performance.
“In the second-half, we had to go and put the game to bed if you like by being a bit more decisive in our final pass and having a bit more forward running to change the speed a bit and I think we got there.
"The thing for the team tonight after the weekend was to show much more quality in possession and make more passes and less simple errors and they did that.”
For left-back Ridvan, it was his first Rangers goal, and Beale was happy with his contribution alongside Abdallah Sima as they caused problems for Livingston this evening.
He continued: “It was a wonderful goal, he is a great character and, in his time here at Rangers he has never really had a run where he has been fully-fit and able to show what he can bring but I thought tonight he brought good energy.
"Both him and Abdallah down that left side were that bright spark for us and probably the difference between the two teams overall because all of our good play came down that side.
“I don't think they have had a shot on target, and you know with Livingston they will make it difficult, they'll play forward, set-plays and things like that so look we are delighted.
"You have to beat the team that is in front of you, it's the third game in seven days, it is a quarter-final so always your energy is not going to be top, but we stayed with the ball a lot more tonight.
“We need to keep possession to work the other team to take their legs away and to make them come out because I felt at the weekend, we were too cheap in possession, and it left us vulnerable tonight there was none of that.”
With the semi-final draw seeing Rangers drawn against Hearts, Beale gave his initial reaction, adding: “Alex Lowry got them there obviously and I am delighted for him last night. It was a good personal moment for him to score, it will be a tough game. I think both semi-finals are really good.
“We actually play them the week before at Ibrox in the league so it will be a busy week again, but it is a game we are looking forward too. We are going to Hampden and we want to make sure we do well that day when it comes around to go back for the final.”