Nigeria international Victor Osimhen scored the opening goal in the 26th minute, giving Galatasaray the lead.
Midfielder Lucas Torreira doubled the lead just three minutes before halftime, and forward Roland Sallai made it 3-0 early in the second half.
Konyaspor managed to pull one back in the 53rd minute through Pedrinho, but Sallai scored his second goal just two minutes later.
Forward Yusuf Demir sealed the win with a fifth goal for Galatasaray late in the match.
Galatasaray will now wait for the result of the match between Trabzonspor and Goztepe to determine their opponent in the championship.