Kiev purple patch crushes Kazan
Rubin scored the only goal before the interval through an Alejandro Dominguez free-kick in the 25th minute as Dynamo struggled to impose themselves on the match.
The arrival of Tiberiu Ghioane and Oleh Gusev off the substitutes' bench lifted Dynamo's performance and Ayila Yussuf finally opened the scoring for the home team in the 71st minute, heading a Gusev corner into the net.
Brazilian Gerson Magrao scored his first goal for Dynamo after a cross from Ghioane through Andriy Shevchenko eight minutes later. Gusev scored the third five minutes from time.
Shevchenko, Ukraine's most famous striker and a former European Footballer of the Year, was playing his first game in European competition for Dynamo since his free transfer switch from Chelsea.
"We needed to change things around and Gusev became our trump card despite fitness problems," coach Valeriy Gazaev told reporters. "Our substitutions had a great impact and reinforced our attack with speed and quality."