UPDATE 1-Soccer-Silva scores for both sides as Milan go third

* AC Milan win 2-1 at Lazio to climb to third

* Milan's Brazilian centre back Silva scores for both sides (Adds details and byline)

By Paul Virgo

ROME, Nov 8 (Reuters) - Brazilian centre back Thiago Silva scored for both sides on Sunday when AC Milan climbed to third in Serie A with a 2-1 win at troubled Lazio.

The centre back nodded in an Andrea Pirlo free kick from the left to put Milan ahead in the 22nd minute with his maiden Serie A goal.

His compatriot Pato also used his head to good effect to put away a Ronaldinho cross and make it 2-0 10 minutes before the break before Silva unluckily deflected a Mauro Zarate shot into his own net in the 65th minute to set up a nervy climax.

The visitors held out under pressure to continue their recovery from a shaky start with a win that gives them 22 points from 12 games.

They are two points behind second-placed Juventus, who won 5-2 at Atalanta on Saturday, and six adrift of champions Inter Milan, who entertain AS Roma at home in Sunday's late game (1945 GMT).

Lazio coach Davide Ballardini is now in serious danger of losing his job as his side have not won in the league since August and were hammered 4-1 at Villarreal in the Europa League on Thursday.