Swansea owed their 1-0 win to Federico Fernandez's first goal for the club, the ball striking the Argentina defender's shoulder after Villa goalkeeper Brad Guzan had failed to collect Gylfi Sigurdsson's 53rd-minute free-kick.
It was far from a vintage Swansea performance, but the win moved them 11 points clear of the Barclays Premier League relegation zone and within touching distance of securing another season of top-flight football.
"It is my first home win and maybe this is the most important victory of the season, so I am very happy," said Guidolin, who was back in the Swansea dugout after missing three matches with a chest infection.
"I know the performance was not very good but this is the match I was waiting for.
"I know the situation and I saw my players' nerves come across in their performance.
"We got the goal and that was the most important thing.
"But in the future for the club, the fans and everyone involved we need to make sure we are not in this situation again.
"It is nearly finished, but not quite."
Swansea improved after a wretched first half following the introduction of midfield veteran Leon Britton.
"After the first half I asked them to play more aggressively and without nerves and we were better," said Guidolin.
"We were better in the second half and having Leon there made a difference,
"He stabilised the team, he won more second balls because we suffered in those situations in the first half.
"We had the attitude of a cup final, and they are never pretty games - but the result is what matters.
"We need to play with this character but with more freedom.
"I want to see this, if we can play this way we have the chance to have good results and finish the season well."
Villa were worth at least a point on the balance of play with Joleon Lescott and Jordan Ayew passing up good scoring chances.
But Villa's sixth successive defeat left them 12 points from safety following Norwich's earlier win at West Brom and in a seemingly impossible position to avoid the drop.
"I think we quite controlled the game, the first half especially," said Villa manager Remi Garde.
"But without scoring in that period you will have a tough time second half.
"The disappointment is that we didn't score.
"They shot once on goal and scored
That is hard to take, but I am pleased with the spirit.
"Until mathematically it is not possible why should we give up?
"We have shown the opposite of teams that give up."
Source : PA
Source: PA