The Premier League leaders, who notched up a record 20th successive Champions League match without defeat, will still be confident of progressing in the second leg at Old Trafford, especially if Inter produce a similarly lacklustre performance.
United were on top from the start with the electric Cristiano Ronaldo going close with three free kicks, one expertly saved by Julio Cesar.
The Portuguese winger also had a header blocked from a Ryan Giggs corner.
Lone United striker Dimitar Berbatov headed wide and Giggs shot straight at Cesar when clean through for the fearless visitors, who made a mockery of Jose Mourinho's belief that they would come to defend.
Inter coach Mourinho, who sprang a surprise by starting inexperienced Colombian Nelson Rivas at centre back, watched on helplessly as his side continually wasted possession in the final third.
The Serie A leaders, who have a disappointing recent record in the Champions League and were knocked out by Liverpool at this stage last season, barely mustered a shot on goal in the first period.
The frustration was so much that Inter substitute goalkeeper Francesco Toldo was booked for remonstrating with the referee from the bench amid another round of loud San Siro groans.
Inter improved after the break with Adriano dragging the ball wide from a good position. Moments later the big Brazilian forward fell in the box but the referee turned down appeals for a penalty.
United injury doubts Jonny Evans and John O'Shea were fit to play in defence and England striker Wayne Rooney started on the bench.
The second leg takes place in Manchester on March 11.
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VIEW! Inter 1-1 United photo gallery from 1999 quarter-final
