Logano made it look pretty easy in the first stage until he started coming up on lapped traffic with six laps to go in the stage.
Bowman, who started the race in 20th, was able to work his car up through the field and got to within a couple of car lengths of Logano for the lead by the final lap of the 60-lap Stage 1.
Erik Jones followed in third with Aric Almirola, who started on the front row alongside Logano in fourth.
Kurt Busch, who scraped the wall and suffered minor right-side damage to his No. 1 Chevrolet on Lap 42, was able to rebound late and finish fifth.
Martin Truex Jr. also challenged Logano for the lead at times, was sixth with Kyle Larson, Chase Elliott, Paul Menard and Brad Keselowski rounding out the top 10.
At the start of the race Joey Logano led the field to the green flag but was passed in Turn 3 by Denny Hamlin who led Lap 1.
Logano was able to get back by Hamlin on Lap 4 bringing Menard with him in second place with Logano leading up until the competition caution on Lap 21.
Kevin Harvick was forced to make an unscheduled pit stop for a potential loose wheel, falling a lap down.
Logano led 57 of the 60 laps in Stage 1 as he continues his quest for second win of the season.