Having dominated the first half the Reds found themselves trailing to Yohan Cabaye's 43rd-minute strike.
But Suarez, who had been a threat throughout the opening period, sparked the Reds into life after the break and scored a brilliant equaliser after controlling a long ball from Jose Enrique with his shoulder before dribbling around goalkeeper Tim Krul.
Suarez underlined his all-round danger to Newcastle when Magpies captain Fabricio Coloccini was shown a straight red card for a foul on him late on.
The 25-year-old has now scored seven goals in his last nine league matches - more than half of Liverpool's total for the entire season.
Rodgers cannot afford to contemplate where Liverpool would be without him and offered fulsome praise on another stand-out performance.
"I thought he was unplayable. Coloccini getting sent off was frustration," said the Reds boss.
"I don't think he could get near him [Suarez] today [Sunday], and he's a good defender, Coloccini.
"He has been a great player over these last number of years for Newcastle.
"Suarez is so bright, so clever, he's a world-class striker. On that form today [Sunday] he really frustrates and provokes defenders.
"He has a hunger for the game, he has a hunger for goals."
The only downside to the performance was that, once again, Liverpool could not finish off their numerous opportunities.
"It's five draws in 10 league games and of those draws we should have won at least three of them," admitted Rodgers.
"That is the margins we are working to at the moment.
"I thought our performance was outstanding. We were terrific.
"First-half our possession and intensity was relentless but we switched off just before half-time."
Newcastle manager Alan Pardew saw his side extend their run at Anfield without a league win to 18 matches.
Cabaye's goal gave him hope they could end that sequence and although he went to speak to referee Anthony Taylor on the pitch at the final whistle he had no real complaints about the red card.
"It was a tough day for us. I honestly felt that when we scored the first goal it would win the game," said Pardew, who said he did not think they would appeal Coloccini's sending-off."
Pardew added: "We had made it very difficult for them, as sharp as they were because they passed and moved the ball really well, and I felt we could get that second goal on the break.
"I went to see the ref at the end because I wanted to see what it [the red card] was for. He said it was dangerous intent.
"Looking at the video it doesn't look too good from one angle in particular.
"I don't think there is any malicious intent but it doesn't look good and we may have to accept it.
"But I don't want to make it a big issue about the referee.
"Morale for referees must be really low because of what is going on [regarding Chelsea's complaints about Mark Clattenburg] and so I had no problem with his performance, which was spot on.
"It was a tough game to manage."
Pardew has injury problems mounting up after James Perch - likely to be out for a month with a thigh strain - Cabaye and Demba Ba all went off.
"It would have been a really bad day today if we'd lost three players (to injury), lost our captain and lost the game so at least something went for us at the end," he added.