The left-back then caught Victor Moses late and was sent off after 68 minutes.
Chilwell's 68th-minute dismissal for two yellow cards allowed Chelsea to push forwards and Kasper Schmeichel saved Marcos Alonso's stoppage-time free-kick.
"Obviously we all feel a little bit exhausted, past year we went from week to week, but now we have already played a lot of games".
Evans' early header set West Brom on its way to halting a 20-game run stretching back to August, with fellow defender Craig Dawson heading in at the start of the second half.
"I am happy with our game of course", he said.
"We tried to create chances and score".
"We didn't suffer defensively".
On the negative side, while Antonio Conte's squad have remained relatively unscathed by injury there is a creeping sense of unease among Chelsea supporters that the lack of respite is starting to affect the Blues boss and his players. It did not pay off.
On Alvaro Morata, the Italian gaffer absolved the striker of any blame despite him not scoring since Boxing Day.
Conte said it was normal for Chelsea's manager to face speculation about their position
Conte says our attacking struggles are down to the whole team and not any one individual. At the same time we're showing not great quality in our finishing.
This weekend's Super 6 fixtures all come from the Premier League and we have looked into our crystal ball as we bid to win the jackpot with Sky Sports.
What won't help this perception either is the fact that Saturday's 0-0 draw with the Foxes was, bizarrely, Chelsea's third goalless game in a row - something which has never happened in the club's history.
Asked if more could be read into their conversation, Conte added: "No, not other situation or other conversation".
"It's good news. Now I don't know the time he needs to recover".
Conte last summer signed an improved contract, but not an extension to his deal which expires in June 2019, and there has been continual speculation over his position.
Leicester were relentless, playing like champions, with the intensity of their pressing forcing mistakes.
"It is mixed feelings".
"Perhaps we deserve another result".
The London side had lost just one of 11 league matches before Saturday and claimed another three points when Bakary Sako's first-half strike eluded Nick Pope. It was harsh but it was good to keep the point at the end.
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