The Belgian midfielder - recalled to the side after being left out of the midweek Champions League win over Schalke for disciplinary reasons - converted after referee Andre Mariner pointed to the spot for what looked like a fair shoulder challenge by Steven Reid on Ramires.
It was rough justice on West Brom, who had looked set for another memorable away victory to add to their success at Manchester United in September after second-half goals from Shane Long and Stephane Sessegnon.
Injured Baggies goalkeeper Ben Foster posted "load of s***" on Twitter, but manager Clarke tried to remain composed.
"I am flabbergasted at the decision, I cannot believed the referee gave it," said Clarke.
"What is the point (of talking to the referee)? I cannot change the decision.
"He (Ramires) started going down early before the contact, so you guys can put a label on it if you want.
"For me the onus is on the referee to make the correct decision and he did not make it.
"The referee has to be 100 per cent sure it is a penalty, and how he can be 100 per cent sure in that instance is beyond me. It was a bad decision."
Former Chelsea assistant coach Clarke added: "It is the kind of penalty which can be given when you have got a home crowd which shouts for everything and puts pressure on the referee.
"Referees are human, they can make mistakes like everyone else."
Chelsea, who lost at Newcastle last weekend, had gone in front just before half-time through another poachers goal from Samuel Eto'o after defender Liam Ridgewell delayed his clearance.
However, West Brom where level on the hour through Long's header and then Chelsea keeper Petr Cech allowed Sessegnon's shot to squirm into the net, which had looked enough to take all three points until the late drama.
"We had a plan to play and for the first half we did most of that right to frustrate Chelsea, but we did not show enough ambition to go forwards and got mugged just before half-time on the goal," Clarke said.
"We responded well in the second half and were the better team, so I am disappointed that a decision has cost us two points and it is not the first time this season.
"Hopefully it will not cost us in the long run."
Jose Mourinho - who had not lost any of his previous 65 Premier League home games in two spells as Blues a manager, winning 51 - was in no doubt the referee had made the right call for the penalty.
"It is difficult for the team that is winning to accept because you are waiting for the last whistle and the penalty comes. But a penalty is a penalty, whether it is minute 94 or minute one," he said.
"This one was a penalty. From the bench, I did not know, I was too far away, but from looking at the (replay) screen, there are no doubts."
Mourinho felt West Brom's second goal should have been disallowed for a foul on Branislav Ivanovic.
"It is a big free-kick, just in front of the fourth official," he said.
"That's where I think the fourth official's job, instead of looking to see if the manager is in his technical area or not, he should participate in the game."
Mourinho was delighted with the response of his players to secure a point.
"After their second goal, our reaction could have been we die or we fight for life, and the team fought for life and threw everything into attack," he said.
Mourinho also praised the calmness of Hazard to cap a positive end to what had been a difficult week.
"Penalties are easy to score in training sessions - I score - as they are when you are winning 3-0 or 4-0, but this was a difficult one and the kid was very calm," he said.
Cesar Azpilicueta was again preferred at left-back to Ashley Cole.
Mourinho said: "Azpilicueta is playing very well. He was (first-choice) today, let's see what happens next week, but again he played with zero mistakes."
Clarke, meanwhile, was looking forward to catching up with his old mentor once the dust had settled at Stamford Bridge, having been on the receiving end of a "manly kiss" from the Portuguese after Chelsea's late equaliser.
He said: "We will respect each other's opinions. We won't speak about the penalty. We will speak about each others families."