Seeing his first action since his tour de force performance winning Wimbledon, the Spaniard took a moment to find his footing on the Canadian hardcourt. But the outcome was never in doubt, stretching his winning streak to 13.
"I try to be focused on every match, I try not to think about the winning streak just to keep going like I am doing," Alcaraz told the sold-out Toronto crowd.
"I always say the first match in every tournament is never easy. It's even tougher playing against Ben, big bombs, big serves, big shots.
"It was trouble to get my good rhythm but I am pretty happy to get through and have another chance."
Alcaraz was slow out of blocks as he shook off some competitive rust, fighting off three break points before holding serve in a tense eight-minute first game.
But the Spaniard, a perfect 10-0 in first-round contests this year, was soon in command, with Shelton helping Alcaraz's cause by double-faulting on break point in the fourth game to gift his opponent a 3-1 lead that was all he would need to clinch the opener.
Alcaraz was far from on top form but the 41st-ranked American, who has only one career win over a top-10 opponent, could not take advantage, misfiring on chances when he had them.
In the second set, it was Alcaraz showing frustration, gesturing to his box and talking to himself after missing shots that are normally automatic winners when he is operating in a higher gear.
Neither player could manage a break chance, sending the set to a tie-break where Alcaraz's experience in the big moment came through. He reeled off four straight points after Shelton won the first, taking it to 7-3.
Next up for Alcaraz is Poland's Hubert Hurkacz, who was a 5-7 6-3 6-0 winner over Serbia's Miomir Kecmanovic.
A pair of 36-year-old veterans, Scot Andy Murray and Frenchman Gael Monfils, rolled back the years and into the third round with contrasting wins.
Monfils upset fourth-seeded Greek Stefanos Tsitsipas 6-4 6-3, while Murray, a three-time champion in Canada, battled past Australian Max Purcell 7-6 (2) 3-6 7-5.
Second-seed Daniil Medvedev, competing for the first time since losing to Alcaraz in the Wimbledon semi-finals, dominated proceedings from the baseline during his 6-2 7-5 win over Italian qualifier Matteo Arnaldi.
Eighth-seed American Taylor Fritz, who followed up his Atlanta title with a run to the semi-finals last week in Washington, advanced with a 7-6(7) 3-6 6-3 win over Frenchman Ugo Humbert.