* Argentina forward ends scoring drought with double
* Busquets nets rare goal in 3-1 win over AC Milan
* Barca into last 16 with two matches to spare (Adds quotes, details)
BARCELONA, Nov 6 (Reuters) - The familiar sound of his name echoing around the Nou Camp signalled the end of a mini goal drought as Lionel Messi scored twice in a 3-1 win over AC Milan that put Barcelona through to the Champions League last 16 on Wednesday.
Alarm bells had been ringing from the Catalan capital to the World Player of the Year's native Argentina and beyond after Messi failed to score in four consecutive La Liga outings, a barren run by his sky-high standards.
He grabbed his first with an emphatic strike from the penalty spot on the half hour, prompting the Barca fans inside the giant arena to begin the chants of "Messi, Messi, Messi" that have marked so many of his home appearances in Europe's elite club competition.
An unmarked Sergio Busquets nodded in Xavi's free kick 10 minutes later but Gerard Pique turned the ball into his own net moments before the break to make it 2-1 and give Milan hope.
The Italian side looked more threatening after Mario Balotelli replaced Robinho at halftime before Messi made a trademark dash between the defenders and dinked the ball over goalkeeper Christian Abbiati for his second seven minutes from the end.
It was the 26-year-old's sixth goal in three games in Europe this season and his 65th in 82 Champions League appearances and firmly put to bed concern he might have lost his cutting edge after a couple of brief injury absences.
Barca's comfortable victory lifted the Group H leaders to 10 points from four matches and put them through to the knockout round with two matches to spare.
Milan, struggling in both domestic and continental competition, have five points in second and Ajax are third on four after they won 1-0 at home to Celtic in Amsterdam.
"Mission accomplished," Busquets said in an interview with Spanish television broadcaster Canal Plus.
"I think we played a good first half and the own goal right at the end was a pity," added the Spain international.
"We suffered a bit in the second but we had chances for a third and when it came everything was much easier.
"It was only a matter of matches and in front of goal Messi is always a machine. Today he has scored two and I hope he can continue in the same vein."
Barca quickly settled into their customary rhythm, with Xavi and Andres Iniesta pulling the strings in midfield and Messi, Neymar and Alexis Sanchez roving up front.
Alexis came close to an opener in the 21st minute when he just failed to get enough on a Neymar centre to turn it into the net before the referee ruled Ignazio Abate had hauled the Brazilian down in the area.
Messi smashed the penalty straight down the middle and was engulfed by his team mates, obviously delighted their talisman was back on the scoresheet.
Milan captain Riccardo Montolivo clipped a swerving shot narrowly wide five minutes later but the visitors' was caught napping when an unmarked Busquets headed into the net from Xavi's free kick.
An impressive Kaka surge down the left wing led to Milan's goal when his low centre skewed off Pique's foot and past goalkeeper Victor Valdes.
Milan coach Massimiliano Allegri brought Italy forward Balotelli on for Robinho at halftime and his physical presence lifted the visitors.
They enjoyed a lot more possession without really threatening and Messi brought the supporters to their feet when he exchanged passes with substitute Cesc Fabregas and finished with his usual aplomb to put the game beyond the seven-times European champions.
"We knew we were facing a great team which keeps possession well and make it tough for their opponents," Milan midfielder Andrea Poli said on UEFA.com.
"However, I think we played well especially when we were 2-1 down and we created a few chances to equalise," he added.
"We wanted to earn points tonight but I think we played a good game anyway. I think we could do better on the counter attack. Now we have to focus on the next two decisive games."
In the next round on Nov. 26, Barca play at Ajax and Milan are at Celtic before Barca host the Scottish champions and Milan are at home to Ajax on Dec. 11. (Writing by Iain Rogers in Madrid, editing by Ed Osmond)
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- Lionel Messi
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