The 22-year-old netted twice to help the Latics clinch a 3-0 victory over Doncaster Rovers at the DW Stadium on Tuesday night.
Colclough was subsequently substituted on the hour mark and, still in his full Wigan kit, made it to hospital just 30 minutes before his second son, Harley Thomas, was born.
"I saw my dad come right out down to the bottom of the stands and he sort of just gave me the action that the waters had gone, and then I knew that I needed to get off as soon as possible," Colclough told Sky Sports News.
"It's a little bit surreal... I looked over to my dad and saw him say 'get the message to the manager' - but then before I knew it I was in the box and I'd scored. I just celebrated because I knew what was coming and before I knew it I was off the pitch and on my way to the hospital.
"I got there as quick as I could, there was no time for getting dressed. And as soon as I got there it was literally 30 minutes later I had my son in my arms. I think my son made it a hat-trick for me!"
Doncaster defender Joe Wright opened the scoring with an own goal as the Latics moved to within a point of League One leaders Shrewsbury Town.