* Third league win of season for Milan
* Cagliari rally to defeat Catania 2-1 (Adds quotes, details)
By Terry Daley
ROME, Oct 19 (Reuters) - A stunning long-range strike by Valter Birsa helped AC Milan end their poor run of Serie A form with a scrappy 1-0 home win over Udinese on Saturday.
In the day's other match Cagliari came from a goal down to beat 10-man Catania 2-1 on their return to the Sant'Elia stadium after an 18-month absence.
Birsa gave injury-ravaged Milan, who were without a host of players including striker Mario Balotelli, their third league win of the season following a 22nd-minute counter attack.
Despite a far from convincing display during which Brazilian Kaka made an uneventful 20-minute cameo appearance, Massimiliano Allegri's side leapfrogged Udinese into eighth place with 11 points from eight games.
"We need to maintain this spirit which we lost a bit at the start of the season," said Allegri.
"Tuesday is going to be a really tough match. We need to play perfectly," he added, referring to the Champions League clash with Barcelona.
Milan had stand-in Brazilian goalkeeper Gabriel to thank for brilliantly tipping Antonio Di Natale's 64th-minute free kick on to the crossbar.
He stepped in at the last minute after first-choice Christian Abbiati dropped out with a calf injury.
"This win will give us a boost. We will be taking on probably the best team in the world but we want to make it a great game," said Milan midfielder Andrea Poli.
Catania took a deserved lead in Sardinia through Gonzalo Bergessio who headed home a powerful opener from a fifth-minute corner.
Cagliari soon got over their homecoming nerves though and the outstanding Victor Ibarbo levelled 21 minutes later with a fine individual goal.
Ibarbo spun away from defender Nicola Legrottaglie before firing a fizzing shot past Alberto Frison from a tight angle.
The Colombian should have gone on to give his side the lead with a penalty four minutes before halftime.
Ibarbo was pulled down by Legrottaglie, who was sent off for his clumsy challenge, but he missed the resulting penalty and the followup header from Frison's save.
Mauricio Pinilla then sent the crowd into raptures with the winning goal, tapping home from his own rebound after hitting the post before charging into the stands to celebrate with supporters who had packed into the north end of the ground.
Cagliari's win was the perfect postscript to a stadium saga which meant the club were barred from playing at two venues before being forced to play their home games 1,000-km away in Trieste.
The team from Sardinia occupy 10th position in the table while Catania are fifth from bottom. (Editing by Tony Jimenez)