Elsewhere, 1966 European Cup runners-up Partizan Belgrade lost 2-1 at Belgian league champions Racing Genk while Dutch side Twente Enschede eased past Romanians Vaslui 2-0 thanks to a double from Austria striker Marc Janko.
The third qualifying round winners are battling for a spot in the play-off matches where they could seal a berth in the competition proper.
In Ukraine, Alan Kasaev struck from close range in the sixth minute to give Rubin the lead before Bebras Natcho added a second goal for the Russians with a 68th-minute penalty.
Shevchenko was left sitting on the bench as an unused substitute while Dynamo failed to capitalise on a host of scoring chances. Coach Yuri Semin's team will now have a mountain to climb in next week's return match.
The two teams also met in the Champions League group stages two seasons ago, Dynamo winning in Kiev 3-1 before holding Rubin to a 0-0 draw in Kazan.
In Belgium, Genk came from behind to earn a 2-1 home win over Serbian opponents Partizan thanks to a superb injury-time goal from late substitute Marvin Ogunjimi.
The striker, who came on in the 85th minute, sent a vociferous home crowd into raptures when he controlled a deep, searching pass and beat goalkeeper Vladimir Stojkovic with a delightful lob from 10 metres.
TWO SENT OFF
Genk defender Calvin Anele Ngcongca was sent off for violent conduct in the 32nd minute but Partizan also had forward Stefan Babovic dismissed shortly after the interval for two bookable offences.
Nemanja Tomic had put Partizan in front but the same player also gave away a soft penalty five minutes later that was converted by Jelle Vossen in the 70th minute.
In Enschede, two-goal Janko led Twente to victory over Vaslui in a match played at the Gelredome in Arnhem.
Twente were unable to use their home ground after a roof collapsed at the stadium earlier this month, resulting in the death of two construction workers.
Janko converted a penalty after 34 minutes before adding a second goal after the break.
In Scotland, 1979 European Cup runners-up Malmo won 1-0 at Rangers thanks to a 18th-minute goal from Daniel Larsson.
In other matches, Lithuania's Ekranas Panevezys drew 0-0 at home to BATE Borisov of Belarus while FC Zestafoni were held to a 1-1 draw in Georgia by Sturm Graz of Austria.
Slovakia's Slovan Bratislava drew 0-0 in Cyprus against APOEL Nicosia and Polish side Wisla Krakow triumphed 2-1 at Litex Lovech of Bulgaria.
There are eight more qualifying games on Wednesday including former European champions Benfica hosting Trabzonspor and Panathinaikos travelling to Odense BK.
