It would be nice if a two-way defensive effort like Sunday’s NFC championship — a game in which New York Giants quarterback Eli Manning took what seemed like a season’s worth of hits and his counterpart, the 49ers’ Alex Smith, seemed constantly under siege — didn’t pivot on a mistake, let alone a pair of them, by a single player.

Yet even as the Giants celebrated their second trip to the Super Bowl in five seasons, the search for heroes led directly to a goat, second-year wide receiver Kyle Williams of the San Francisco 49ers, who turned the ball over on not one, but two punts — one in the fourth quarter, one in overtime — in his franchise’s most important game in a decade.

The box score will show that the Giants’ 20-17 overtime victory was decided by Lawrence Tynes’s 31-yard field goal with 7 minutes 6 seconds remaining in the extra period. The season summary will show that it was the Giants’ fifth straight victory, a run of success that seemed improbable the week before Christmas, when they were a .500 outfit. And it will show that Manning, who took six sacks, brought his team back from a deficit in the fourth quarter and completed 32 of a staggering 58 passes for 316 yards and two touchdowns.

But Manning summed up the feeling while the teams exchanged punts as if they were in a ping-pong match, as rain pelted the players and fans at Candlestick Park: Don’t screw up, because maybe they will.

“Just kind of: Be patient, don’t force anything,” Manning said. “That’s what I kept telling myself.”

Williams’s first miscue came with the 49ers holding a 14-10 lead completely provided by their relentless defense and tight end Vernon Davis. The Washington native, who put San Francisco in this position with a last-minute, drilled-as-he-caught-it 14-yard touchdown catch to beat New Orleans a week earlier, hauled in a 73-yard touchdown pass in the first quarter, sprinting away from two defenders to open the scoring. He came back with a 28-yarder, just when it seemed that the 49ers couldn’t move the ball through a sopped piece of paper, to give San Francisco a four-point advantage in the third quarter.

By the time Williams dropped back to field Steve Weatherford’s punt — the teams combined for 22 punts on the day, a testament to their superior defenses — the rhythm of the game had been determined. Williams let the ball bounce, then tried to skitter out of its way. The problem: It hit his right knee. Barely, but it did. Giants receiver Devin Thomas — the former Redskin — recovered with 11:08 left in the game.

Six plays later, on third and 15 from the San Francisco 17, Manning found Mario Manningham on a post pattern. The Giants were up, 17-14.

“Eli just keeps hanging in there, hanging in there, hanging in there,” Giants Coach Tom Coughlin said, “and made plays when we needed them.”

Smith countered by working the 49ers into position for David Akers’s 25-yard field goal, which tied the score with 5:39 remaining. The two teams seemed at a stalemate. Each finished regulation with 319 yards of total offense.

“Just a classic football game that seemed like no one was going to put themselves in position to win,” Coughlin said.

The game was befitting of these two old NFC stalwarts, franchises that met for the eighth time in the playoffs, though it was the first contest in nine years. Those matchups include the Giants’ 15-13 victory in the NFC championship game following the 1990 season, memorable for Roger Craig’s fumble, recovered by Lawrence Taylor, that led to Matt Bahr’s winning field goal. They include the 49ers’ 39-38 wild-card victory after the 2002 season, memorable for the errant snap from New York long snapper Trey Junkin on what would have been the winning kick.

The 49ers now have a similar gaffe. After San Francisco defensive end Justin Smith sacked Manning for the final time, Williams dropped back to field another Giants punt on their second overtime possession. This time, he made the catch. But a rookie linebacker named Jacquian Williams extended his arm as Williams flew by.

Williams, with the ball in his right hand, couldn’t hold on. The ball popped out, onto the sloppy turf. There, Thomas pounced on it. Candlestick, so rowdy through all the downpours, grew quiet. The Giants had the ball at the San Francisco 29. They all but had the game.

“Everybody knew we were going to get a break,” Manning said. “We were going to have a chance to win this game.”

They worked the ball to the middle of the field. Manning knelt on second down. Tynes kicked on third. And when the ball sailed through the uprights, the Giants had a date with New England — a rematch from four years ago. And Williams, the 49ers and the city of San Francisco had an offseason to think about the punts that cost them a trip to the Super Bowl.