Chelsea dominated the first half and took the lead when John Terry headed home from a corner.
Suarez nodded a leveller with just under 20 minutes remaining and though the Reds had chances to go on and claim all three points during an excellent finish, they wouldn’t have been too downhearted as they left the capital.
Liverpool went into the game having recorded successive league doubles over their hosts, a statistic which gave Roberto Di Matteo cause to classify the Reds as a ‘bogey team’ in his pre-match press conference.
His side almost made the ideal start in shaking off that tag when Joe Allen lost possession in midfield in the sixth minute, inviting Eden Hazard to play Oscar through on goal. The Brazilian was under pressure from Andre Wisdom but should have tested Brad Jones, who was again standing in for the injured Pepe Reina.
Operating with three center-backs, Liverpool controlled the early possession, but it was Chelsea who looked most threatening in the final third.
Branislav Ivanovic was next with an attempt, arrowing over from 30 yards.
The opener came from a Juan Mata corner after 20 minutes when Terry, afforded room to spare at the near post, powered a header beyond the reach of Jones.
It might have been 2-0 seven minutes later when Hazard ran clear of Allen in midfield before side-footing to Fernando Torres. The Spaniard tried to place the ball beyond Jones but was denied by a good reaction stop before Hazard skewed the rebound.
The closest Liverpool came to any kind of response was a drive along the ground from Nuri Sahin. Wide.
The game was brought to a lengthy stop 10 minutes before the interval when Suarez stumbled out of a challenge and into Terry, whose leg was bent backwards in the collision. The former England skipper left the field on a stretcher and was replaced by Gary Cahill.
The disruption did little to alter the flow of the game, and again it was Chelsea who came the closest to finding the net prior to half-time when Mata went one-on-one with Jones. A few seconds later he was smacking the turf in frustration after directing the ball over the crossbar.
Liverpool was in need of a spark, but it was Chelsea who was first to probe after the break, Mata not coming as close with a long-range effort as the gasps from the home crowd suggested.
Jones displayed excellent reflexes to stop Torres heading home his first goal against his former employers since departing in January 2011. The save prompted a round of pinball in the Liverpool box but those in red eventually cleared their lines.
Brendan Rodgers replaced Sahin with Suso just before the hour mark, and while the impact wasn’t instant, the 18-year-old was to play his part in an equalizer that hadn’t looked likely. It was his corner in the 72nd minute that was flicked from the near post to the far by Jamie Carragher. Suarez reacted quicker than Ramires and, from a yard or two out, nodded home before celebrating in front of the travelling supporters.
From here the game could have gone either way, and Suso might have won it for Liverpool had he shown a little more composure from a Raheem Sterling cross.
Suarez had Petr Cech scampering back to his goal line with an effort from just inside the Chelsea half, while Ivanovic almost headed the winner from a corner.
Enrique then played Suarez clean through but Cech was quick off his line and got a decisive touch.
The final chance for the hosts was created and executed by Hazard, who angled just wide of the top corner. At the other end Suarez gave an onrushing Jose Enrique the chance to shoot towards the bottom corner but the effort was saved.
Liverpoolfc.com man of the match: Brad Jones.