With Rangers now four points ahead of their title rivals despite playing one game more than Celtic, the ex-Liverpool captain said his team would stay on the ground for the title after registering two consecutive league wins at Celtic Park For the first time since 1995.
Rangers defender Connor Goldson scored twice in each half to help the Gers fashion a big win over Celtic in the derby at the home of their most hated rivals.
Neil Lennon didn't have some of his top players to pick out and even I could admit the game was going to be tough, but that performance even surpassed my wildest non-expectation.
The Bhoys were missing a host of players as Hatem Abd Elhamed, Nir Bitton, Christopher Jullien, Ryan Christie and Odsonne Edouard were all ruled out.
He said Sky Sports: "We showed a really controlled, professional performance".
"We could maybe have scored more", he added. We will not get carried away.
Rangers got the start they wanted when Goldson escaped his markers from Tavernier's searching free-kick and flashed a header past goalkeeper Vasilis Barkas.
Mohamed Elyounoussi insists the absence of supporters from today's Old Firm clash at Celtic Park will not minimise the importance of the fixture.
Lennon pointed to his lack of options with James Forrest also out injured, while Albian Ajeti and Leigh Griffiths were not match fit.
"We were pretty decimated with the Covid and the injuries but I felt we had a strong enough team out".
"The Scottish teams, I don't think they should be trifled with just because it's not the Premier League", McLeish told Football Insider.