Jimenez netted his third goal of the season in the 58th minute having been teed up by Daniel Podence, who had twice been denied by goalkeeper Lukasz Fabianski earlier in the second half.
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After a drab first 45 minutes where only a Kurt Zouma header that rocketed back off the crossbar threatened either goal, Olivier Giroud put Chelsea ahead when his effort squeezed through Rui Patricio and was awarded by goal-line technology.
It was all thanks to goals from on-loan teenage wingback Rayan Ait-Nouri and Daniel Podence