Hume, who was sidelined for almost nine months with a fractured skull following a challenge by Sheffield United's Chris Morgan last November, scored the Tykes' second goal from the penalty spot shortly after the half hour as Roberto Di Matteo's promotion challengers were put to the sword.
The strike was warmly received by the home supporters inside Oakwell and Robins was keen to add his own praise after the final whistle.
"I'm delighted for Iain because it has been a long time coming," said the Barnsley boss.
"As a striker you live off your goals and even though he has been working hard for the team and putting in good performances you need the goals for your self-confidence.
"I've certainly got confidence in him, the supporters love him and he's working his socks off and deserved his goal.
"I didn't watch it but it was nice to hear the crowd react when it hit the back of the net."
Adam Hammill had earlier fired the Tykes into a deserved lead and their victory was ensured when Shelton Martis diverted a cross into his own net with 10 minutes remaining.
Barnsley move out of the relegation zone as a result and Robins added: "I'm a happier manager than I was on Saturday (when they lost 5-2 at QPR), put it that way.
"The players have put on a really good show and I thought we were good value for the win.
"I'm not getting carried away but it was a really professional performance.
"We've set a standard and we need to maintain that. It's fantastic (to move out of the bottom three) and it certainly gives us a platform but we don't want to go and spoil that by putting in a below-par performance on Saturday (against Ipswich)."
Albion boss Roberto Di Matteo was infuriated by his side's display, despite seeing them grab a late consolation through Chris Brunt.
"It was terrible," moaned the Italian. "We didn't do anything that we were supposed to do, especially in the first half.
"You can't allow any team all that space. We made them look good."
The Baggies have now suffered three consecutive defeats in league and cup since their stunning 5-0 victory over Middlesbrough earlier in the month.
And Di Matteo added: "I think we'll have to sit down on Thursday and talk about it because you need to get the basics right.
"It has probably been the worst game for my team. We need to pick ourselves up and start again.
"It's a tough league. We've said that all along and it's proven to be the case."