Henderson left the team hotel on Tuesday to be with his partner as she gave birth but promised Rodgers he would not miss the FA Cup sixth round replay at Blackburn's Ewood Park.
The Liverpool skipper played the entire match on Wednesday, setting up Philippe Coutinho for the only goal in his team's 1-0 triumph, which sent them into the semi-finals.
Rodgers was full of praise for Henderson's commitment to both his family and Liverpool.
"Jordan Henderson actually had to go back from the hotel - his partner had their second child during the night, so he had gone away, hadn't slept so much and travelled back again and put in a performance like he did tonight, a real captain's performance," Rodgers said at his post-match media conference.
"Some players maybe would have missed the game, but he said to me: 'Boss, as soon as the baby's out I'll be coming back!' There was a car waiting!
"He spent time with his young partner, child and family, which is great, but he said, 'I'll be back' - and he was.
"He had his lunch, he had a good sleep this afternoon and then played like a real captain."
Rodgers also confirmed both Mamadou Sakho and Daniel Sturridge will need further medical assessment after being substituted at Ewood Park.
"We'll see [with Sakho] in the morning," the 42-year-old said.
"He felt his hamstring tighten, so we'll just need to see it.
"Daniel Sturridge had a bit of tightness, so we took him off and we'll assess that tomorrow."
