But the Giants had to feel anything was possible after an improbable victory in which everything that could go wrong did, yet they still won.
With their fifth win in eight games, the Giants moved within four games of idle Colorado in the National League Wild Card race. Both teams have 12 games remaining.
They got a short start from Barry Zito, tallied only one run-scoring hit while going 1-for-11 with men in scoring position and virtually scored the winning run on an inning-ending double-play grounder.
Oh, and as if that weren't enough, Brian Wilson closed it out with two strikeouts on one pitch.
Wilson was the last of five relievers who picked up Zito with 4 2/3 innings of three-hit shutout pitching.
Bengie Molina's tiebreaking single in the fifth was the Giants' lone run-producing hit of the night. San Francisco had taken a 1-0 lead in the first when Arizona second baseman Ryan Roberts' error on Pablo Sandoval's grounder allowed Freddy Sanchez to score from third. The Giants added a fourth-inning run on Eugenio Velez's RBI infield grounder and made it 4-2 on Aaron Rowand's sacrifice fly in the fifth.
Pinch-hitter Fred Lewis somehow beat out a hard smash to second with the bases loaded and one out in the eighth to allow the tiebreaking run to cross the plate.
And after all that, Wilson brought down the dramatic curtain by essentially ringing up both Chris Young and Justin Upton on one full-count slider.
The right-hander delivered that pitch to get Young looking for the second out in the ninth inning. Stephen Drew followed with a sharp single to left to bring up Upton, whose two-run single in the fifth had chased Zito.
With the count 3-and-2, Upton fought off three tough fastballs, fouling each away. Then he took another heater that split the plate for the game-ending out.
"The slider had to be in the back of his mind," conceded Wilson, "and that's definitely what I wanted to do [with the full-count slider to Young], to make him think I could throw the breaking ball in any situation. That way, he can't sit on one pitch."
All night, none of the Giants teetering on the edge of the playoff picture could sit comfortably. Especially not upon seeing Lewis, batting for Kevin Frandsen with the bases loaded and one out, rip Esmerling Vasquez's 1-and-2 pitch at second baseman Augie Ojeda.
Bochy was hoping.
"It was Fred Lewis running. That's why I hit him; he's tougher to double up than Frandsen," Bochy said. "Thank goodness for speed."
Lewis beat shortstop Drew's relay to first by a half-step, as Travis Ishikawa came home from third with the run that made it 5-4.
"I thought it'd be a close play," Lewis said, "so I just tried to get down the line as fast as possible. I had fresh legs."
They gave the Giants fresh life, and fresh hope.
"It was a great win for us," Lewis said. "Our pitchers kept us in that game."
Before Wilson nailed down his 35th save, Jeremy Affeldt muted the eighth for his Majors-leading 32nd hold. And before that, there were earlier bullpen contributions by Bob Howry (1 2/3 innings), Dan Runzler (two-thirds of an inning) and Sergio Romo (two-thirds).
"Our bullpen ... what a great job they did," Bochy said.
Following Mark Reynolds' two-run homer in the first, Zito kept the D-backs down until Upton delivered a two-run single with one out in the fifth that tied it at 4 and also chased the left-hander.
"Z threw the ball well, I thought. But in the fifth, it caught up to him, and it put us in a tough situation," Bochy said.
They are still in a tough situation, four down with two weeks to go.
"But we still believe we are in this thing," the manager said. "We do need to get a little help. But we still have a chance at the postseason, and that's all we're thinking about."
It was easier to think about that at the end of a night when the Giants went 1-for-11 with men in scoring position and still scored five runs.
This is the sort of thing that can make otherwise-rational men feel that fate, maybe, is on their side. That they're "chosen."
"If we were up four or five games, I might think that," Bochy said with a wry smile. "But we're four back, so, no. But there's still hope."
That's all Bochy had as Lewis was making his way down the first-base line, so who knows how far hope can take you?