Angels score it all in the first en route to 4-0 victory over Seattle

Reporting from Seattle — As much gloom has filled their June — and we’re not just talking about the overcast skies and 58-degree temperatures at Safeco Field on Tuesday night — the Angels still have this going for them:

They play in the forgiving American League West, a division so unimposing from top to bottom that it could qualify for an act of Congress: No team left behind.

Even with the Angels notching their 4,000th win in franchise history Tuesday night, a 4-0 victory over the Seattle Mariners, they are 4-8 in June and have scored three runs or less in nine games.

But after Jered Weaver threw a five-hitter for his fourth career shutout and the offense bunched five hits in a four-run first inning, the Angels (33-36) are only 31/2 games behind the first-place Texas Rangers, who at 36-32 have the worst record of baseball’s six division leaders.

The Mariners (34-34) have one of baseball’s least potent offenses, and they are only two games out. Even the woeful Oakland Athletics, who have lost 13 of 14 games, are within striking distance.

“You look at the standings and you do think that — it’s been a rough couple of weeks and we’re still 31/2 games out?” right fielder Torii Hunter said. “You try to stay away from that stuff and focus on what you have to accomplish.

“I definitely think if we play better baseball, we execute and do all the right things, we’ll give ourselves a chance to win. If we falter in any way, if we don’t execute, we’re going to have problems.”

If the Angels gain some momentum from their first back-to-back wins since May 29-30, they should benefit from playing in what is arguably baseball’s weakest division, one that no team appears capable of running away with.

“The other teams have been struggling too,” designated hitter Bobby Abreu said. “That’s good for us.”

Weaver was great for the Angels on Tuesday, the right-hander striking out six and walking one to improve to 8-4 on the season and 11-4 in his career against Seattle.

He threw a career-high 128 pitches, 82 for strikes, and has thrown 115 pitches or more in eight of 15 starts, a heavy workload some fear may be too taxing.

Not Manager Mike Scioscia, who sent Weaver out for the ninth even though he threw 115 pitches through eight.

“We’ve gone a little deeper at times, but he’s certainly capable of going into the 120s,” Scioscia said. “The main thing is mechanics and how he rebounds. If he’s out of his mechanics and struggling, you [pull him]. But we thought he had enough in his tank, and Jered finished strong.”

The Angels offense started strong, providing a four-run cushion before Weaver, who received zero runs of support in his previous two road games, took the mound.

Erick Aybar opened the first with a double to left, and Hunter hit a run-scoring single to left. Abreu walked, and Vernon Wells’ fielder’s-choice grounder put runners on first and third for Howie Kendrick, who hit an RBI single to right.

Russell Branyan’s RBI single to right made it 3-0, and Peter Bourjos doubled to left with two outs for a run and a 4-0 lead.

Seattle starter Doug Fister blanked the Angels on two hits over the next six innings, but the Mariners, who are hitting a league-low .228, rank 13th in the AL in runs and last in on-base and slugging percentage, mustered nothing against Weaver.

“The four runs in the first wasn’t startling — it was awesome,” Weaver said. “Any time you get a four-spot in the first you’re going to feel more comfortable. It takes some pressure off your shoulders. You can fill up the strike zone with fastballs and mix your off-speed stuff in later in the game.”

mike.digiovanna@latimes.com