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It took the Italian, who yesterday knocked out 13th seed Mikhail Youzhny, almost three hours to defeat his Spanish opponent in a close affair.
Andujar will wonder how he lost the first set as he broke Seppi twice to move into a 5-2 lead but couldn't serve it out.
Seppi reeled off four games in a row to move 6-5 ahead before Andujar regained his composure to force a tie-break.
In a see-saw breaker, Seppi won four points in a row to move 4-1 ahead but then Andujar did the same to go 5-4 up before Seppi closed it out with three more consecutive points.
In the second set both men had multiple break-point opportunities but couldn't take them and it looked like another tie-break would be needed.
However, in the 12th game Andujar snapped Seppi's serve to clinch the set and take the match into a decider.
Both men were strong on serve in the decider, but Andujar cracked once and the only break in game seven was all Seppi needed to complete victory, wrapping the match up 6-4.
Eight-time Monte Carlo champion and top seed Rafael Nadal is Seppi's opponent in the third round.