Shakhtar dominated possession as expected but were toothless up front and Inter opened the scoring with their first chance after 19 minutes.
Real, Barca and Juve stand firm on Super League
The win pulled Inter on level with Napoli. Both have 22 points, six behind leaders Juventus, and Inter have the better goal difference, although positions are ultimately decided on the head-to-head record.
IMAGES from the UEFA Champions League matches played on Tuesday.
Holders Inter Milan progressed to the semi-finals of the Italian Cup when they beat Lazio 1-0
AS Roma thrashed Parma 4-0 at home to cut Inter Milan's lead in the Italian Serie A to six points.
Real Madrid coach Jose Mourinho's quest to become the first man to win the European Cup with three different clubs will include a super-charged visit to Milan following Thursday's draw for the Champions League group stage.
Premier League champions Manchester City were drawn on Thursday with Juventus, Wydad AC and Al Ain in Group G for next year's FIFA Club World Cup in the United States.
AC Milan beat a 10-man Inter Milan to stay in the race in \n\nthe Serie A league.\n\n
Inter Milan have been fined 15,000 euros after fans chanted racist slogans about their former striker Mario Balotelli during a Serie A match on Sunday.
AC Milan surged up to joint second in Serie A thanks to Filippo Inzaghi's hat-trick in a 5-1 home thrashing of lowly Torino on Sunday.
Inter have got through two-legged ties in all nine of their previous meetings with Olympique Marseille.
Claudio Marchisio blew open the Serie A title race when his superb goal gave 10-man Juventus a 2-1 win over leaders Inter Milan in an enthralling game on Saturday.
Serie A clubs AC Milan and Inter Milan are being investigated as part of a probe into suspected accounting fraud in Italian soccer.
Inter Milan began their Serie A title defence with a 1-1 home draw with Udinese on Sunday after an Ivan Cordoba own goal in injury time, while AC Milan won 3-0 at promoted Genoa helped by Kaka's brace.
European champions AC Milan beat Lazio 1-0 at the San Siro on Sunday to join Juventus at the top of Serie A.
In another match in the Amsterdam tournament, Ajax held Liverpool goalless.
Inter Milan moved into the Italian Cup quarter-finals with a 2-0 victory over second-tier Verona on Tuesday.
European champions Barcelona will face Inter Milan, Dynamo Kiev of Ukraine and Russian newcomers Rubin Kazan when they open the defence of their crown following the draw for the Champions League group phase on Thursday.
He also finished the season five goals clear of the next leading scorer, Cristiano Ronaldo of Juventus.
Barcelona's Cameroon striker Samuel Eto'o has agreed personal terms with Inter Milan, his agent said on Thursday as a swap deal involving Zlatan Ibrahimovic moved closer.
AC Milan were held 2-2 at struggling Torino on Sunday, leaving city rivals Inter Milan three points clear at the top of Serie A. Torino's Alessandro Rosina scored a 78th-minute penalty, which was conceded for handball by Kakha Kaladze, to earn the hosts a draw after Ronaldinho had put Milan 2-1 up with a spectacular free kick in the 34th.
Chelsea will look extremely familiar to Inter Milan coach Jose Mourinho for more reasons than one when the pair meet at the San Siro on Wednesday in their Champions League last 16 first-leg clash. Mourinho won two Premier League titles as manager of the London club while the two sides are very similar in style.
AC Milan reached an agreement with Barcelona on Saturday to bring former Inter Milan striker Zlatan Ibrahimovic back to Italy in a move the club hope will ignite their title chances.
Barcelona top the LaLiga standings with 15 points, four ahead of Real Madrid and Villarreal. Girona are seventh on seven points.
Two goals from Ronaldinho helped AC Milan to a 3-0 win at toothless Juventus on Sunday which piled the pressure on Juve's rookie coach Ciro Ferrara.
Inter Milan signed Ricardo Quaresma from Porto on a five-year deal on Monday after the Portugal winger passed a medical, the Serie A champions said on their website (www.inter.it).
Internacional forward Paolo Guerrero missed a late penalty and then had a goal disallowed as his side were held 1-1 by Athletico Paranaense in Brazil's Serie A on Thursday.
Fiorentina, two goals down and reduced to 10 men, converted two quickfire penalties to draw 2-2 with AC Milan in Serie A on Sunday while a 12-minute hat-trick by German Denis gave Atalanta a 4-3 win at a stunned Inter Milan after they had trailed 3-1.
Zlatan Ibrahimovic moved from Juventus to Italian rivals Inter Milan for $31.95 million.
Kevin Prince Boateng scored the first goal and impudently set up Robinho for the second to help rampant Serie A leaders AC Milan to a 3-0 win at troubled club Bologna on Sunday.
Real Madrid will present Jose Mourinho as their coach on Monday after agreeing an undisclosed compensation deal with Inter Milan, the Spanish club said on Friday.
A spectacular piledriver from Juan Cuadrado gave Serie A leaders Juventus a 1-0 win over Inter Milan, ending a run of seven successive Serie A wins for their opponents in a pulsating end-to-end match on Sunday.
A fabulous backheel from Zlatan Ibrahimovic helped Inter Milan to a 2-1 home win over Bologna on Saturday and put the Serie A champions back on track after an awkward week.
The 21-year-old Nigerian international, who joined Inter in 2002, has scored six goals in all competitions this season.
Al-Nassr have appointed Stefano Pioli as manager to replace Luis Castro, the Saudi Pro League club said on Wednesday.
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