Guidolin was able to breathe a big sigh of relief after his Tuesday's 1-0 home victory over Genoa.
The result was their second success of the campaign and the first time Udinese had kept a clean sheet this season.
Guidolin's joy was understandable as he had come under fire with his side having previously picked up four points in the last four games.
"We deserved the win," Guidolin said. "I am happy because I have seen improvements with respect to our previous games.
"My players showed more intensity and determination against Genoa and these are positive signs."
Udinese have yet to win on the road this campaign.
"We know that sooner or later the win will arrive," Guidolin said. "We came close in Verona last weekend (when Udinese lost 2-1 to Chievo) but we ended up conceding our second defeat of the season."
Rivals Atalanta conceded four first-half goals in Wednesday's 4-3 loss at Parma.
The outcome was the Bergamaschi's third straight defeat and Atalanta coach Stefano Colantuono could not hide his disappointment.
"We made too many mistakes in the first half," Colantuono said. "We tried to get back in the game after the re-start but thedamage had already been done.
"Now we must turn the page and focus on a difficult game against Udinese."
Atalanta have won just once this campaign and lie 17th in the standings with just three points.
The visitors hope to recover Colombian striker Luis Muriel, who sustained a muscular injury in training on Wednesday and is doubtful to feature on Sunday.