Victory against Dundee restores Celtic's 25-point advantage over Aberdeen at the top of the table with nine games remaining.
A first half strike from Jozo Simunovic and a second half header from Stuart Armstrong seemed to have the Hoops cruising to victory at Dens Park.
However, a superb strike from substitute Faissal El Bakhtaoui gave Dundee hope and made for an exciting finish on Sunday.
The Glasgow giants were put on the back foot as Dundee pressed for an equaliser and were forced to take off winger Scott Sinclair and bring on centre-half Erik Sviatchenko to help defend their lead.
Celtic withstood the late pressure and Rodgers was happy to see his players show a different side to their game as they extended their unbeaten domestic run to 36 games.
"I thought we showed a lot of different elements to our game today," Rodgers said.
"We played some good football at times and had good control of the game. We never created too much in the first half but we still deserved to be in front.
"In the second half we scored a great goal. It was perfect in terms of the build-up play and construction.
"I just felt that after that we had some more chances to close the game out and we probably just lost our positioning a little bit in order to keep the ball.
"Obviously at 2-1 we had to show a different side because it was quite direct from Dundee. So, we had to defend the box, we had to compete, we had to win our headers and win second balls, and the players did that.
"It was a very good victory for us. Parts of the game were very good but other parts we had to show fight and a strong mentality. It was an important three points."
Victory restores Celtic's 25-point advantage over Aberdeen at the top of the table with nine games remaining and means the Hoops could claim a sixth successive title with victory away to Hearts on April 2.
Dundee's Paul Hartley watched his side lose out to Celtic by a single goal for the third successive game following a 1-0 defeat at Dens and a 2-1 loss at Celtic Park earlier in the season.
Hartley praised his players for the spirit they showed in the match.
"We had to withstand a lot of pressure in the first half but we knew they would have a lot of the ball," the Dundee boss said.
"But I thought out shape was good and our organisation was good.
"We conceded a poor goal in the second half but after that we went and had a go. We changed the shape and Haber had an excellent chance, we got an excellent goal from El Bakhtaoui and we put Celtic under pressure.
"They ended up changing to a back three and brought on a centre half so credit to the players in the second half for how they fought and never gave in."