The Lions were simply ripped apart by a rampant home side who netted all four goals inside 35 minutes, former Hearts captain Danny Wilson setting the ball rolling with the opener before a Martyn Waghorn brace and Kenny Miller effort had the points wrapped up by half-time.
Substitute Liam Buchanan’s effort ten minutes after the restart, though, restored some pride to the visitors’ camp in what was a much-improved second-half display.
Hopkin admitted he feared the worst for his players having conceded four times with still 45 minutes to play, but a change in both tactics and personnel brought a more resilient showing from the West Lothian strugglers.
“We were completely overwhelmed in the first half,” Hopkin said. “I thought Rangers started the game with a great tempo and we struggled to cope with it. For the first 20 minutes it could have been any score. I changed a few things at half-time and asked for a performance in the second half and I think I got it. I don’t think many teams will come here, keep the ball... we scored a goal, we could have had another one or two so I was delighted.
“I said to the boys at half-time that I didn’t want it to become six or seven. I had three strikers playing the second half and changed the system and I think Rangers struggled a wee bit. We scored a great goal so I am taking the positives in that we won the second half 1-0.”
He continued: “You can’t come to Ibrox and have three or four not performing. I made the decision to change it up and we were definitely better in the second half. We always knew this was going to be a tough game with the way they’ve been playing, scoring five or six goals recently. We’ve got to concentrate on the teams around us.”
Despite the heavy snow making conditions far from ideal, Mark Warburton’s men were fast out of the blocks and had control in the eighth minute when Waghorn’s initial shot was deflected into the path of Wilson, who calmly headed past Marc McCallum in the Livi goal from a couple of yards.
With the Lions defence all at sea, Miller then raced through on goal but just as he was about to pull the trigger, a superb last-ditch tackle from Declan Gallagher prevented the former Scotland internationalist from getting his strike away.
However, a neat turn of pace from Miller in the box was subsequently halted by Gallagher and referee Craig Thomson pointed to the spot. Waghorn duly converted from 12 yards in sending McCallum the wrong way.
Livi were fortunate not concede a second penalty in a matter of minutes as Barrie McKay’s curling effort clearly struck the hand of Ben Gordon, Thomson waving away claims much to the relief of the former Alloa defender.
Lee Wallace’s pass into the path of Miller from the left touchline found the striker in acres of space and he took one touch to control before sending a shot across goal and into the far corner for number three.
Waghorn then somehow hit the post from a yard before he made amends with a deft chip over McCallum for the hosts’ fourth of the afternoon.
Buchanan and Danny Mullen were introduced for the second half and the former made an immediate impact with a crisp finish into the left corner from the corner of the box to reduce the deficit.
Mullen brought out a smart stop from Wes Foderingham as the Lions grew in confidence but McCallum still had to be alert to deny Nicky Law’s stinging shot at the other end.
Morgyn Neill hauled down Dean Shiels in the final minute to give Rangers a second penalty of the afternoon, but with Waghorn having already been substituted, Andy Halliday couldn’t convert the spot-kick as McCallum got down low to thwart the midfielder with a tremendous block.
Rangers: Foderingham, Tavernier, Kiernan, Wilson, Wallace, Law (Zelalem 68), Halliday, Holt (Shiels 77), McKay, Waghorn (Clark 67), Miller. Subs: Bell, Ball, Forrester, Thompson.
Livingston: McCallum, Neill, Gordon, Gallagher, Longridge, Gibbons (Mullen 46), Fotheringham, Stanton, Pittman, Glen (Buchanan 46), White (Currie 80). Subs: Jamieson, Halkett, Knox, Sheerin.
Referee: C Thomson.