Winless in their opening three games in the second tier following relegation from the Premier League, the Hammers have won three times in eight days to storm up the table.
Bowen's decision to remain in east London was a massive boost to West Ham's hopes of bouncing straight back to the Premier League.
"I want to score goals, get assists and get points for the team and tonight was perfect," said Bowen.
"We knew it wasn't going to be pretty to come and win the game, but the main thing was to win the game and we've done that."
The England international opened the scoring after 13 minutes, but Bolton levelled through Ethan Erhahon and then went in front thanks to Ruben Rodrigues' penalty.
Konstantinos Mavropanos quickly levelled for the visitors when he headed in an Arne Engels free-kick.
Bowen finally decided the game 13 minutes from time but needed a helping hand from Bolton goalkeeper Gavin Bazunu, who spilt his shot into the net.
Swansea were toppled at the top of the table on goal difference after their unbeaten start came to an end in a 3-1 defeat at Southampton.
Finn Azaz, Cyle Larin and Leo Scienza were on target for the Saints, who are already in the top half despite starting the season with a four-point deduction.
Burnley moved off the foot of the table but are still waiting for their first win of the season after a 1-1 draw at Wrexham.
Rounding off the results, Cardiff and Stoke City drew 1-1, while Preston and Blackburn both lost 2-1 to Sheffield United and Watford, respectively.