The Lions lost eight line-outs on their own throw in Christchurch, and if there is no improvement, they will probably kiss goodbye to the Test series.
"Donncha is a bit like Gavin Henson, in that he has had a fantastic tour and is one of those players when he was picked (for the squad), I believed would make his mark on the tour," said Woodward.
"I am very glad he is here. We had a poor night last Saturday, (Danny) Grewcock has now left us, and Donncha has got to take his opportunity, along with Paul O'Connell, who has been given another chance.
"It is a big opportunity for both the Irish guys."
Leinster hooker Shane Byrne misses out, but Ireland flanker Simon Easterby makes his Lions Test debut.
Lewis Moody comes in at open-side flanker to offer a third jumping option.
The Lions are taking an attacking approach to the second Test and Moody starts ahead of Neil Back because of his all-out commitment and action-packed style that Woodward hopes will keep the side going forward.
Prop Graham Rowntree, a long-time team-mate of Moody's with Leicester and England, backed him to make the required impact on New Zealand, and their destructive open-side Richie McCaw.
"I've always thought Lewis is an awesome player," said Rowntree.
"When he's in top form, he's an incredible player and shows absolutely no respect for his body with the things he does on the field. He'd be in my team any day of the week."
Corry, who took over the captaincy after Brian O'Driscoll was stretchered off, drops to the bench as Ryan Jones takes over the number eight shirt.
Jones and Easterby have both been in inspirational form since arriving late on tour but Rowntree feels Corry is unlucky to have lost his place in the starting line-up.
"Coz is a warrior and we need warriors," Rowntree said.
"It's not only what he does on the field, it's what he brings to the build-up as well - he's a big cog in things.
"Without doubt, the team had to be changed - the result was that disappointing - but I thought there was room for Coz.
"Having said that, he can come on and make a difference - I hope we both can."
Rowntree, a touring Lion to South Africa in 1997, is on the bench again but admits he had little chance of shifting Gethin Jenkins from the loose-head prop role.
"You always want to start, but I don't think Gethin or Julian White deserved to be dropped," he said.
"How frustrating was it to sit on the bench? On a scale of one to 10? It was 20. And it was freezing."