Launch from the Baikonur Cosmodrome and landing 200 km southeast of Karaganda.

This mission was a rendezvous flight with Vostok 4. Both spacecrafts came close to 6.5 km (visibility), although the Vostok capsules had no maneuvering capability. They quickly drifted apart. Vostok 3 also conducted several scientific observations and further improvement of the space ship systems, communications (spaceship ground control and spaceship to spaceship), guidance and landing. There were no problems with his spacesuit, but there was only a minor problem with the Tral telemetry system.

During his first day in orbit, Andriyan Nikolayev unstrapped himself from his seat and became the first spacefarer to float freely in conditions of microgravity in space

Andriyan Nikolayev's orbital companion Pavel Popovich was launched the next day aboard Vostok 4. Data on the two spacecraft's orbital parameters that were released periodically by Soviet news agency TASS seemed to indicate a change in Vostok 3's orbital trajectory within ten hours of Vostok 4's launch, leading to speculation that the former spacecraft modified its orbit to bring it closer to that of the latter. The Vostok spacecraft is not believed to have had the ability to modify its orbit. Plans were for the spacecraft to approach to 5 km (3.1 mi), but the closest distance achieved was 6.5 km (4.0 mi). At the start of Vostok 3's thirty-third orbit this distance had diverged to 850 km (530 mi), and to 2,850 km (1,770 mi) at the start of the sixty-fourth.

Andriyan Nikolayev and Pavel Popovich made contact with one another via shortwave radio soon after their spacecraft approached one another; they would maintain regular ship-to-ship communications over the course of their mission in addition to their contact with the ground. Andriyan Nikolayev reported sighting the Vostok 4 capsule after it entered orbit near him

Both Andriyan Nikolayev and Pavel Popovich spent time out of their seats each day, conducting a series of tests to determine their ability to maneuver and work in conditions of weightlessness. Each test was said to last "about one hour". The physical and mental state of the cosmonauts were monitored: biometric sensors relayed the cosmonauts vital statistics to the ground; the cosmonauts' behavior and coordination was observed via a cabin-mounted video camera; and the cosmonauts' ability to perform various operations in coordination with ground controllers was considered. The cosmonauts' speech was monitored both by controllers on the ground and one another. The results of the tests were deemed positive, evidence of the ability of humans to function and work over longer periods in microgravity.

A final "first" for Vostok 3 was Andriyan Nikolayev's taking of color movie footage of the Earth from orbit and from the cabin interior.

The reentry was the same procedure as in the other Vostok missions.