The couple married in November 2019 after being seen many good times with Bautista Agut during his tennis matches around the world.
Earlier in the tie, Shapovalov had won his match with a 6-4, 6-3 scoreline against Pablo Carreno Busta.
Bautista Agut kept piling up the pressure, as he finally emerged victorious following a high-quality two hours and 44 minutes of tennis.
Pablo Carreno Busta overcame Serbia’s Filip Krajinovic 6-3, 6-4 to book Spain’s place in the semi-finals at ATP Cup in Sydney.
Alcaraz will make his debut in the competition, and he will be joined by Roberto Bautista Agut, one of the heroes of the 2019 World Cup
The Italian star came from a set down to get past Albert Ramos-Vinolas in the second round of the Western & Southern Open.
Andy Murray's Wimbledon 2021 came to an end, even as other seeded competitors carried on through to the next round of the tournament.
Jannik Sinner came back from a set down to beat seventh seed Roberto Bautista Agut in the semi-finals of the Miami Open.