He did just that, flirting with history along the way.
Eovaldi threw seven-plus scoreless innings in his home state, yielding just two hits and a pair of walks in a 3-1 win over the Rangers.
The Alvin, Texas, native had a no-hitter through six, but lost the bid when Rangers OF Nomar Mazarra led-off the seventh with a single.
Outside of that, though, Eovaldi was near-spotless on the evening, striking out six on 98 pitches in his first victory of the young season.
He didn't receive a ton of run support, but then again, his outing didn't entail it.
After squandering a bases-loaded opportunity in the second, the Yankees grabbed a couple in the top of the third -- courtesy of a solo home run from Jacoby Ellsbury and an RBI double from Mark Teixeira.
They added to their advantage in the sixth, when Starlin Castro contributed his own solo shot on a fly ball to left.
In all, the Yankees were just 1-for-9 with runners in scoring position, leaving eight men on base. But their performance was enough to beat Texas lefty Cesar Ramos, who -- starting in place of injured ace Cole Hamels -- allowed three earned run in six innings.
In fact, if there was one dark spot for the Yankees in this one, it was their bullpen. Dellin Betances entered in the eighth and surrendered a solo blast to Brett Nicholas, ruining the right-hander's perfect ERA.
Andrew Miller, however, was as good as always, working a 1-2-3 ninth for his fifth save in as many opportunities.
WHAT IT MEANS: The Yankees improved to 8-10 on the year, having taken the opener of a nine-game road trip. They remain in the cellar of the AL East, three back of the division-leading Orioles.
NEXT UP: The Yankees and Rangers continue this series on Tuesday. Luis Severino (0-2, 4.86 ERA) and A.J. Griffin (2-0, 3.18 ERA) are slated to be your starters, with first pitch set for 8:05 p.m. ET.