After sweeping away the struggling Rockies and Nats, the Mets found themselves across from an actual contender to score a ticket into October. They showed up Sunday in danger of getting swept away themselves for the first time this season, and in their own home no less.

The team with the major’s best ERA and the National League’s best record was in need of a well-pitched game after the relievers failed to provide much relief in the opener and after Tylor Megill’s start went badly in game two.

Griffin Canning didn’t give the Mets what they were seeking in the series finale. Nor the bullpen. And the hitters took Father’s Day off.

The Mets managed three singles off Shane Baz over his 6 2/3-inning outing and finished with five hits.

Tampa Bay completed the three-game sweep, winning 9-0 in front of sellout crowd of 42,804 at Citi Field.

The scrappy Rays (39-32) have now beaten the Mets (45-27) in 14 of the 17 games they have played dating to July of 2018.

Before this latest game, manager Carlos Mendoza was talking up the rotation despite Kodai Senga suffering his Grade 1 hamstring strain Thursday and the inconsistency of Megill.

Besides bringing that top-ranked overall ERA of 2.88 to the stadium, the Mets’ starters owned a major league-leading 2.82 ERA.

“Senga goes down, it hurts, obviously,” Mendoza said. “But overall I feel good, especially with guys like [Frankie] Montas, Sean [Manaea], where they’re at in their rehab process. We have some reinforcements coming, too. But we’ve got to keep going and we feel good with what we have.”

Canning (6-3) arrived with a one-year deal and an inflated 4.61 ERA compiled over five seasons with the Angels. The 29-year-old righty has deflated that number with the Mets, although it rose from 3.22 to 3.80 after this start.

Actually, four of his last five starts haven’t been too impressive.

When this day was done, Canning had been charged with six runs, all earned, four hits and five walks, plus one wild pitch that allowed a run to come home.

Tampa Bay put together a small-ball, three-run rally when they struck first in the second — full-count walk, full-count walk, bunt single, RBI fielder’s choice by Kameron Misner, run-scoring wild pitch, RBI single lined into left by Danny Jansen.

The Rays nicked Canning for another in the third — four-pitch walk, ground single to right by Jonathan Aranda, RBI fielder’s choice by Jake Magnum.

The Mets stranded a runner in scoring position in the first, then had another chance to do damage against Baz in the third.

Luisangel Acuna grounded a single into center with one gone. Francisco Lindor followed with a walk. After Brandon Nimmo went down swinging, Juan Soto drew a walk to fill the bases for Pete Alonso.

Baz (6-3), who walked four and hit one, fell behind 3-and-1, then got Alonso to swing and miss on back-to-back fastballs. The second one arrived at 99.2 mph.

The free passes came back to hurt Canning again in the fifth. He walked the leadoff batter, got a fly ball, then walked another. Mendoza walked out to get him.

But Aranda greeted Max Kranick with a liner down the rightfield line for a two-run double.

Junior Caminero rocked a three-run homer to left off Ryne Stanek with one out in the ninth. After Stanek retired the next batter, Mendoza brought in infielder/outfielder Jared Young to try to get the final out.

The “righthander,” throwing in the 50s, 60s and 70s, allowed a single and a walk before getting Misner to fly to center.

Now the Mets head out for a six-game NL East trip, playing three at Atlanta and three more at Philadelphia.

Lindor has been playing on a broken right pinkie toe after being hit by a pitch on June 4 against the Dodgers in Los Angeles. He had a day off from shortstop Sunday, serving as the DH. It was a compromise. Mendoza wanted to give Lindor a full rest. The state of the toe? “It’s all about pain tolerance,” Mendoza said. “He feels like day by day he’s getting better. There’s better days than others. But what I’m getting from the trainers is hopefully in the next couple of weeks, it’ll be a lot better. I don’t think this is something he’s going to have to play through the whole year.” . . . David Peterson, Paul Blackburn and Clay Holmes are the Mets’ scheduled starters for the Atlanta series that begins Tuesday night . . . Mark Vientos will begin his rehab assignment Tuesday with Triple-A Syracuse. The third baseman/DH strained his right hamstring on June 3 in Los Angeles.