It appeared two points would be dropped by Jose Mourinho's men as an entertaining contest looked likely to end goalless until Phil Jagielka was adjudged to have fouled Ramires in the left channel.
Frank Lampard's inswinging free-kick was glanced down by Branislav Ivanovic and captain John Terry, returning from a three-game absence with a gluteal muscle problem, slid in to score past Tim Howard.
"When you score minute 90-something you can speak about being lucky," Mourinho said.
"The reality is that the boys chased that. We were the team that was really trying to win, which is our responsibility.
"We deserved it. I never thought we would score so late. I had hope that we could score a goal before that. Destiny wanted last minute."
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