Mario Balotelli crashed a 25-yard stunner home before Didier Drogba rounded Brad Jones to put Carragher's side 2-0 up.
However, Gerrard netted from the spot in either half to secure a 2-2 draw.
Suarez was not the only former Anfield favourite to return, with Fernando Torres, Pepe Reina and Xabi Alonso all turning out.
Liverpool fans among the sell-out Anfield crowd will have been pleased to see Jon Flanagan and Lucas Leiva get run-outs as they return to fitness.
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