Mexican Jimenez lit up a largely forgettable Premier League affair on the south coast by emphatically ending a 336-day wait to hit the net with a fine moment of individual magic in the 61st minute.
The 30-year-old - sporting protective head gear following his sickening clash with former Arsenal defender David Luiz last November - twice beat Saints defender Jan Bednarek, as well as leaving Mohammed Salisu on his backside, before calmly slotting beyond home goalkeeper Alex McCarthy in front of a jubilant away end.
"This three points and this goal go straight to Raul," said Lage.
"The fans did a fantastic job because they started in the first minutes singing his song. Everyone has given great confidence to him.
"With goals you give happiness to everyone. The face when you win is not the face when you lose. It was a special goal for Raul.
"I saw since the first day that he was a guy with a big ambition and hungry to come back to play to score goals for us.
"Today, it happened but he knows he needs to continue to score goals."
Jimenez feared he may never play again in the aftermath of his horrific head injury at the Emirates Stadium almost 10 months ago and only returned to the field at the start of this campaign.
His milestone strike was a rare piece of quality in the 250th top-flight fixture staged at St Mary's and gave Wolves only a second success of the campaign under their new boss.
Lage, who - like Jimenez - arrived at Molineux from Benfica, was equally impressed by the forward's desire to protect the slender lead.
"Raul is a good example, you can be a top player and a top man," said the Portuguese coach.
"Every time he's there working, working, working to do everything, to understand our way, to press, to help our team.
"And you see after he scored one goal, he stayed 20 minutes running and pressing and helping the team to defend the set-pieces. He's a top player, top man and he knows his job."
Southampton remain without a league win this campaign and faced jeers from sections of the disgruntled home support at full-time.
Nathan Redmond saw a first-half effort disallowed for offside but the hosts - who have now gone eight games without success dating back to last term - once again struggled to create as they failed to score for a third consecutive top-flight fixture.
Frustrated manager Ralph Hasenhuttl admits his goal-shy team have work to do.
"We are all disappointed because at the moment we are a little bit struggling to find the way to the back of the net," said the Austrian, who lost lethal striker Danny Ings to divisional rivals Aston Villa in the summer and replaced him with Adam Armstrong.
"We didn't get a lot of big chances against a team that is defending deep. We had a good moment in the second half, but you need a goal in that moment.
"It's not new that strikers coming to us need a bit of time to adapt to the Premier League. But it's not only strikers, we also have 10s coming in good situations to score.
"We have to do something more."