Hicks hit a three-run home run in the fifth inning of New York's 10-8 victory over the Blue Jays at Yankee Stadium. The Yankees joined the 2002 Texas Rangers as the only teams to hit home runs in 27 consecutive regular-season games.
All-Star Giancarlo Stanton added his first home run of the year, a three-run shot, in the sixth inning.
"It's kind of what we do," Hicks said. "We hit home runs here. That's kind of how we score runs. ... We're doing it as a team, which is huge. Top to bottom is doing damage and that's what we need."
The Yankees began the streak in a May 26 loss to Kansas City. Catcher Gary Sanchez leads the Yankees with eight home runs in that span.
"We have a lot of guys capable of hitting the ball out of the ballpark," Yankees manager Aaron Boone said. "I think they help strengthen each other because collectively they're able to wear down pitchers. That eventually leads to more and more mistakes at different points in the night."
The Yankees set the franchise record for most consecutive games with at least one home run Sunday. Second baseman DJ LeMahieu hit a three-run home run off Astros ace Justin Verlander to pass the 1941 Yankees' record of 25 consecutive games.
The first-place Yankees have a five-game lead over the Tampa Bay Rays in the AL East Division.