World and Olympic champion Farah won the 10,000 metres before Bolt sprinted to a narrow triumph in the 100m, clocking 10.06 seconds at the Mestsky Stadion.
Bolt recently suggested he would carry on competing after August's IAAF World Championships in London, but only for the remainder of this season.
The Jamaican was rusty from the start, but soon showed his trademark surge in the second half of the race to win from Cuba's Yunier Perez. Perez finished in a personal best of 10.09secs.
However, the times were well short of the world lead of 9.82 set by Christian Coleman of the United States in Eugene, Oregon earlier this month.
Bolt, after his ninth appearance in 11 years in Ostrava, was given a special farewell. He was presented to the crowd before the Jamaican national anthem was sung in his honour.
"I'm not happy with the time," Bolt told the crowd. "I'm just getting into my running. I have some training to do to get some good execution. I'll be fine. No worries."
Farah won the 10,000m in 27mins 12.09secs.
Kenya's Mathew Kimeli led Farah as the pair reached the bell in 26:12. The Briton responded down the back straight, kicking to overtake Kimeli and take a commanding lead on to the final bend. He surged to the finish, with Kimeli second in 27:14.43.
Wayde van Niekerk beat Bolt's meeting record over 300m, setting the fastest time ever over the distance. The South African won in 30.81, lowering Bolt's mark of 30.97 set in 2010.
It was also quicker than Michael Johnson's previous world best of 30.85, set in Pretoria in 2000, in a distance which is run irregularly. Isaac Makwala of Botswana was second in 31.44 and Clarence Munyai third in 31.61.
Kenya's David Rudisha, the two-time 800m Olympic champion, was competing over 1000m and finished a disappointing fourth.
Rudisha led into the final 150m, but appeared laboured and was passed in the finishing straight by compatriot Nicholas Kipkoech.
Kipkoech won in 2:18.51.Jakub Holusa of the Czech Republic was second in 2:18.60, with Rudisha finishing in 2:19.43.
