While France's second half performance, in which goals from Franck Ribery and Nicolas Anelka earned them a deserved three points, exuded panache, world champions Italy were a shadow of their normal selves.
France had taken their time to get into the match, but, in terms of possession, they were well on top against a Ukrainian side which clearly lacked the finishing ability of the injured Andriy Shevchenko.
Just after the break, Anelka shot wide of the left hand post as France started brightly and a period of French domination preceded the goal by Ribery in the 57th minute. The 24-year-old, winning his 17th cap, outpaced Ukraine's defence and rounded the goalkeeper to sidefoot home into an empty net.
"I think it was important to win tonight in front of our own fans," Ribery told TF1 television station afterwards.
Domenech added: "Tonight we had the result, the fans, the atmosphere - it was what we expected but I don't think Georgia will be any easier in a few days time."
With 19 minutes to go, Anelka made the match safe. In an impressive piece of individual skill, he jinked the ball up into the air before firing home from an acute angle on the left.
AC Milan striker Filippo Inzaghi scored a brace in torrential rain to give the Italians a 2-0 lead in the match played in Rome, despite the Faroes being the home side. But Rogvi Jacobsen gave the hosts hope of a shock result with a goal 13 minutes from time.
"I'm not going to talk about a bitter victory because when you win, you can't be disappointed," said Donadoni.
"We had many chances but we didn't take them. And if this type of game takes a turn for the worse, when you can't quite score, it doesn't take much for you to find yoursleves in trouble.
"They (Faroes) were never dangerous and they only had one
chance, which they scored from."
Portugal, Serbia bag wins
In other games, Nani scored the opening goal as Portugal won 2-1 in Belgium to cement their place in the top two in group A.
Serbia won 2-0 at Finland to keep pace with Portugal on 14 points from seven games, five points behind leaders Poland, who won 3-1 in Azerbaijan and have played a game more. Finalnd trail Serbia and Portugal by three points after their defeat.
Despite missing four regular starters, including star man Cristiano Ronaldo, Portugal proved too good for the Belgians and despite Marouane Fellaini's equaliser, Helder Postiga hit home the winner halfway through the second period.
"Given the other results it was vital to impose ourselves," said Postiga. "We managed that but it wasn't easy. It was a physical match, not easy at the end of the season."
England's qualification hopes suffered a blow in Group E after wins for their three rivals for the top two spots, Russia, Croatia and Israel.