Due to the pressure of launching Mir in time for the 27th Communist Party Congress, mission planners were left without the newer Soyuz-TM spacecraft or any of the planned modules to launch to the station at first. It was decided to launch an older Soyuz-T as Soyuz T-15 on a dual mission to both Mir and Salyut 7.

Leonid Kizim and Vladimir Solovyov first docked with the Mir space station on 15 March 1986 after their launch on 13 March. Plans for Mir intended that only the newer Soyuz-TM would dock with Mir's forward port, leaving the aft port free for arriving Progress spacecraft. However, the older Soyuz-T was not equipped with the Kurs approach system used on Mir's front port, but only with the older Igla approach system used for Mir's aft port. Therefore, Soyuz T-15 had to approach Mir's aft port, and then manually maneuver around the station to dock manually at the forward port. At 20 km Soyuz T-15's Igla system acquired its counterpart on Mir's aft port. At 200 meters, the Igla system was shut off, and the crew manually maneuvered around the station to dock at the front port. For this manual approach, the same laser range finder was used as for the Soyuz T-13 docking with the uncooperative Salyut 7 station in 1985.

During their nearly 55-day stay on Mir, the crew unloaded two Progress spacecraft, launched after their arrival. The mission was mostly designed to test out the new space station's systems since it had been launched with little scientific equipment, most of which would have to wait for the launch of add-on modules. Despite Mir's name literally meaning "Peace", US officials during this time accused the Soviet Union of performing military experiments on their supposedly civilian space stations. After the cosmonauts' return to Earth, Leonid Kizim in an official press conference stated that Mir was not being used for any military purposes and that "The US is accusing us of this sort of action in order to justify their own plans to extend the arms race into space." The Reagan Administration did not however reiterate these claims so as not to negatively impact the planned 1987 summit meeting between President Ronald Reagan and Soviet leader Mikhail Gorbachev.

In preparation for the trip to Salyut 7, the crew loaded Soyuz T-15 with their personal belongings, plants grown on Mir, and other items. At that time Salyut 7 was still 4000 km ahead of Mir in a lower orbit in the same inclination. Therefore, on 4 May, Mir was lowered by 13 km in order to expedite the approach to Salyut 7 and conserve Soyuz T-15's limited fuel supply for the transfer. On 5 May 1986 12:12:09 UTC they undocked from Mir for their journey to Salyut 7 – at this time, the distance between the two space stations had been reduced to 2500 km due to Mir's maneuver. After a crossing of 29 hours, Soyuz T-15 docked with Salyut 7 on 6 May 16:57:52 UTC