Brazilian Coutinho followed up his fourth round replay winner at Bolton with the only goal at Ewood Park to send Brendan Rodgers' team into a Wembley semi-final with Aston Villa a week on Sunday.
But it has been some 24 hours for Henderson whose wife gave birth to their second child in the early hours of yesterday morning.
Liverpool manager Rodgers praised Henderson - skipper in Steve Gerrard's absence - for playing in the replay after leaving on Tuesday the team hotel in the build-up to the tie to be at the birth.
"There are some players who would not have played but Jordan is not one of those," he said. "He said to me 'as long as the baby pops out in time, I'm playing boss!"
Coutinho broke the stalemate of the sixth round replay with Blackburn in the 70th minute with a superb strike into the far corner of the net after a one-two with Henderson had opened up the Championship club's defence.
And no-one would have been cheering louder than suspended Gerrard who is hoping his last appearance for the club before his departure to LA Galaxy will be at Wembley on May 30.
Rodgers hailed the way his team bounced back following consecutive defeats to Manchester United and Arsenal that seriously damaged their top four hopes.
He said: "I made the point to the players if we could get through to the semi-final it could give us a kick on in league. We have had two poor performances and been criticised. Tonight we performed very well.
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Simon Mignolet saved a last-gasp shot by Blackburn keeper Simon Eastwood
"Over the two games it was a difficult tie. They are strong and well organised. We knew it would be difficult. But my players were brilliant. We created chances."
As for Coutinho's goal, he said: "Philippe is wonderful at that. He sucks defenders in. Great technique. Great goal to win the game."
Liverpool survived an added time scare when Rovers keeper Simon Eastwood – up in support of his strikers - saw a shot saved at the second attempt by Simon Mignolet.
Philippe is wonderful at that. He sucks defenders in. Great technique. Great goal to win the game
Brendan Rodgers
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Blackburn manager Gary Bowyer felt his Championship team should have had a first half penalty when Ben Marshall's header appeared to brush Joe Allen's arm.
He said: "We were disappointed with a decision that didn't go our way in terms of the penalty. [Allen's] arm was out in an unnatural position and he has diverted. It's still a hell of a save from Mignolet.
"I've seen it myself with our analyst: two great saves. I'm very proud of the players. We said we would give it a go and we did.
"To hold Liverpool over two games and have a chance at the end is a great. It shows the progress we have made at the club."
Liverpool's victory came at a cost with Mamadou Sakho and Daniel Sturridge both suffering hamstring injuries.
