Steven Gerrard praised his Rangers side for refusing to hit the panic button against stuffy Kilmarnock.
Alfredo Morelos was the hero as he climbed off the bench to fire the only goal in the 1-0 Ibrox win.
The Colombian's 65th-minute winner – his 28th strike of the season – came at the perfect time to alleviate the growing unease sweeping through the Rangers support.
But Gerrard's team kept their cool to clinch the victory that means they go into Sunday's Old Firm clash five points behind, with a game in hand.
The Ibrox manager – who dismissed rumours linking Rangers with Chelsea striker Olivier Giroud – said: "We have incredible support and, with all due respect, sometimes they come here and just expect you to blow teams away.
"Liverpool supporters were the same when I played there. So it's important to tell the players before the game and at half-time to be patient, continue to believe in what we are doing, not panic or get frustrated.
"I thought we got a little better in the second half, we were shooting more and getting more crosses in. We had more purpose.
"Killie set us a challenge, come and beat us and they made it very difficult for us. We found a way, which is very pleasing.
"I apologise if it didn't look pretty for the supporters, that it wasn't three, four or five goals. But I'm going away very happy because it's a win and a clean sheet.
"We set out to entertain and for it to look brilliant on the eye. But teams are not going to just allow that every single week.
"You have to give credit to Kilmarnock, they defended resolutely. They had no ambition to win the game but we have to accept that teams are going to come here and try to steal points away from us.
"Killie did it very well for a lot of the game and we had to force the goal. So we are learning, but we have to get used to it because a lot of teams will come and do that after the winter break as well."
Had Rangers failed to grab their winner, they would have faced the prospect of falling 10 behind Neil Lennon's champions with a defeat this weekend.
But now Gerrard says his team are heading to Parkhead with the belief they can rein in the leaders.
"We have a game in hand, so I'm not really too concerned about gaps," he said. "I'm concerned with my team winning football matches.
"We are going to Parkhead in good form and good shape. We know it will be a very tough match, they have a very strong home record.
"But we played Celtic a few weeks ago and put a good show on, gave a good account of ourselves. I expect us to go there with confidence and belief we can get a result."
Killie have now lost four games on the spin and are without a goal in their last five.
But interim boss Dyer said: "We were outstanding. They were very good. Everyone worked hard, they were confident, I was chuffed with them – very pleased.
"We were organised, we worked on that the last few days.
"We knew what kind of game it was going to be, we knew they would dominate play.
"It was just about us having discipline and sticking to a game plan and hopefully we would create a couple of opportunities – which we did do.
"It has taken Morelos to come on and win the game for them."