Henry, who is set to make his loan move from Millwall permanent in January, settled Wanderers' nerves with an 81st-minute strike - scoring for the third successive match.
Kevin Doyle's seventh-minute opener had put the hosts on course for an 11th win in 13 league games but they also needed another inspired display from goalkeeper Carl
Ikeme to finally see off an impressive Boro side.
Jackett, whose side remain second in the table three points behind leaders Leyton Orient, said: "I always felt we needed a second goal and I think everyone in the ground felt
that as well.
"It was a quality goal, which I was looking for in the second half from one of my forwards.
"James has come off the wing, found himself central and put it away very well. He's had a bright start to his Wolves career and it does give him something to build on because he knows he can do it here and show his capabilities.
"He's given us another dimension down the right-hand side."
Jackett admitted that the win had a been a tough one and he added: "It was a hard-fought game. Stevenage put us under pressure all the way through.
"We had a lot of possession in both halves and, after an early goal, probably didn't do enough with it going forward.
"They defended their box and their goal very, very well and at 1-0 the game is always open and you know they are always going to keep going as they are a very fit and committed team. So to overcome it and get the three points is a very good achievement.
"It just shows you that you never win games easily. We have a reasonably solid look about us and we have to keep that going.
"We can't take anything for granted whatsoever. It was certainly not comfortable for us, although it was a very good win."
Jackett used the closing stages of the game to re-introduce £5million midfielder Jamie O'Hara after taking him off the transfer list.
O'Hara was met with some boos from the crowd but Jackett said: "I understand the overall situation where he's had some troubles here but I feel enough time has passed where it's really up to him now to prove that he wants to play and contribute to what we're going for this year, which is promotion."