crosscourt forehand wide.
The left-hander Shapovalov struck a crosscourt forehand long to trail 0-40 and face breakpoint.
The Canadian netted a croscourt backhand volley to lose his serve and fall behind 4-5.
Serving for the match, Paul struck a down the line forehand winner to lead 15-0.
Shapovalov netted a crosscourt backhand volley which he followed up with a netted crosscourt backhand to fall behind 0-40 and face matchpoint.
Paul struck a powerful inside out down the line forehand winner to end the match after two hours and 12 minutes of play.
In the start of an eventful week for Paul, he defeated Leo Borg of Sweden in round one 6-4, 6-2.
Borg, the 18 year old son of the 11 time grand slam champion and former number one Bjorn Borg, was making his men's professional tour main draw debut in Stockholm.
Paul in round two defeated the 5th seeded and fellow American Taylor Fritz 6-4, 6-4.
In the quarterfinals, Paul defeated the former number one and former Wimbledon champion Andy Murray of Scotland 6-2, 3-6, 6-3.
Then in the semifinals, Paul upset the 8th seeded Frances Tiafoe of the USA 5-7, 7-6(7-5), 6-4.
In his prior best week on tour, Paul upset the fifth ranked Andrey Rublev of Russia 6-4, 3-6, 7-5 in the third round of the BNP Paribas Open at Indian Wells, California last month in October.