The fouth-ranked Briton chased down wide shots to hit winners and also won points at the net. Bolelli, ranked 43rd, held serve for the first time in the eighth game before pulling out after the following game.
Murray will play Marin Cilic of Croatia, who beat Fernando Verdasco of Spain 6-2, 6-3.
Gilles Simon rallied to beat James Blake 3-6, 6-1, 6-4 to keep the 11th-ranked American winless in five appearances at the tournament.
Blake, who managed only one break in the match, dropped to 0-5 on Madrid's high-paced indoor court.
Simon saved four break points in the second set and converted two of his own before dominating the final set.
French Open semifinalist Gael Monfils of France also advanced, beating Italian wild card Fabio Fognini 6-2, 6-4, while American qualifier Robby Ginepri defeated Michael Llodra of France 6-4, 6-4.
Also, Spanish qualifier Marcel Granollers beat Paul-Henri Mathieu of France 6-4, 6-4, Philipp Kohlschreiber of Germany defeated Carlos Moya of Spain 6-2, 6-2, and Jarkko Nieminen of Finland beat Mikhail Youzhny of Russia 7-5, 3-6, 6-2.
Rafael Nadal, who plays Ernests Gulbis of Latvia later Tuesday, needs only two victories in Madrid to clinch the season-ending No. 1 ranking.
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