In fact, Santos has so much respect for Rivera that he set up a meeting with him through White Sox bullpen coach Juan Nieves during the team's late April visit to New York in order to pick Rivera's brain about the closer's role.
For at least one night, though, the student has surpassed the teacher.
By retiring the Orioles in order during Thursday's 6-3 White Sox victory at Camden Yards, Santos made his 25th straight scoreless appearance on the road to start a season. That Vladimir Guerrero flyout and strikeouts of Matt Wieters and Mark Reynolds gave Santos sole possession of this Major League record, breaking a tie with Rivera, who had worked 24 straight scoreless appearances on the road to begin the 2005 campaign.
Santos didn't even know of the record until apprised postgame by White Sox assistant director media relations Pat O'Connell.
"I knew I hadn't given up a run at all on the road," said Santos, whose road record covers 26 1/3 innings. "But it's one of those things that just kind of happened. I was pitching pretty good and it just so happened on the road."
Thursday's effort marked Santos' 12th straight scoreless appearance overall. He has allowed only two runs since the start of July and has converted seven consecutive save opportunities.
Since back-to-back rough outings on June 8 and June 10, raising his ERA from 1.24 to 3.23, Santos has allowed four runs in 19 innings. That stretch includes 31 strikeouts, three walks and nine hits allowed.
Certainly Santos has a long way to go in just his second full year as a pitcher to establish himself as an elite closer, let alone one of historical excellence such as Rivera. But more records could be in his future if Santos' continues to perform on the mound in a manner which Rivera would approve.
"There's a point where you get tired and get a dead arm and that happens," Santos said. "You have to figure a way to pitch around it and get better.
"I'm lucky and fortunate it's coming together. Throwing strikes, which is my main goal, and I can live with what happens if I'm throwing strikes."