The 33-year-old centre-half broke the deadlock inside two minutes, with Willian doubling their lead before a Jan Kirchhoff own goal put the Blues in complete charge before half-time.
Didier Drogba, who scored the winning penalty to help the Blues win the competition in Munich in 2012, came off the bench to score the fourth before teeing up Brazilian Ramires for their fifth.
And Terry, who was suspended for their victory over Bayern Munich in the showpiece two-and-a-half years ago, heaped praise on the west London side after their empathic win.
Terry posted: “Great win and performance tonight. Top of the group and delighted to be on the scoresheet @willianborges88 @didierdrogba @rami7oficial”
Chelsea booked their place in the Champions League knockout stage courtesy of their 5-0 win.
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