Rangers moved within four points of the league title as Alfredo Morelos fired in a late winner to give them a victory.
Steven Gerrard was sent off at half time but he'll be delighted with how the game finished, having been frustrated throughout the game.
Rangers now need just four points from their final seven games to deservedly clinch the league title and will be looking forward to Saturday's game with St Mirren.
Rangers had to work hard and finally had a half decent chance after 32 minutes when Filip Helander headed over the bar.
Borna Barisic had taken over corner duties and put a perfect ball onto the head of the Swede but he just couldn't get it underneath the crossbar.
Alfredo Morelos then went down inside the box and was fouled by Livingston goalkeeper Max Stryjek but referee John Beaton decided it was a dive from the Colombian and he was shown a yellow card.
Scott Arfield then had a good opportunity but he dragged his effort wide of the target.
There was then controversy at half time as Gerrard angrily approached the referee but Beaton wasn't willing to speak to the Ibrox boss and eventually showed him a red card.
Early in the second half, Goldson then had the ball in the net from a Borna Barisic free kick but the flag went up to rule it out.
There was little opportunities in the second half either and Morelos had one of the rare one with 15 minutes left to go.
Glen Kamara played the Colombian through but he dragged his effort wide of the target. He really should have scored five minutes later when a corner from the left was nodded on and Morelos put it wide.
Morelos isn't often kept quiet for 90 minutes though, and he did get a goal with just four minutes remaining.
It was brilliant work by Davis and Kamara in the build-up and after the former's shot was saved by Stryjek, Morelos was there to tap into an empty net.
Referee frustrations
Gerrard was sent off for reacting angrily but he was right to be annoyed at the decision not to award Rangers a penalty in the first half. Stryjek had clearly connected with Morelos when he went down in the box and it was a stonewall foul.
Beaton decided it wasn't and the yellow card then gives Morelos a bit of a bad name. It is one of the few things you can appeal a yellow card on and you'd imagine Rangers will be straight to the SFA with one on Thursday.
Beaton was probably within his rights to send Gerrard off given the angry reaction but a bit of common sense would have been to calm things down with a conversation.
Rangers probably had a few other decisions they could be annoyed about too and not necessarily match changing ones, but little cynical fouls with Ryan Kent in particular being targeted.
Itten also went down in the box late on but the referee waved play on when he could have awarded a spot kick.
Morelos shows his worth
The Colombian has had his critics at times this season but he's showed his importance recently and grabbed a vital goal at the Tony Macaroni Arena tonight.
He should have had a penalty but he didn't show any frustration and just continued to go about his work. He held the ball up really well and was unlucky not to score at other times.
It's often fired at him that he isn't a natural finisher but he showed his predatory instincts with his late strike.
A year long run
Rangers win now means they've now gone a full calendar year without losing a game. That 1-0 defeat at Ibrox against Hamilton was a real low point for Gerrard but they are now within touching distance of the league title.
They need just four points from their final seven games to win the league and they can do it at Celtic Park.
What a result that would be for Rangers.
