A month ago, the Giants were reeling.

Tom Coughlin woke up on the morning of September 17 as the coach of an 0–2 team, a team that had just been pummeled at home by the Green Bay Packers, a team that appeared to be well on its way to a last-place finish. The biggest question about the Giants was whether they’d fire Coughlin during the season or wait until the end of the year.

And then the Giants staged a come-from-behind victory over the Washington Redskins, and then they beat the Philadelphia Eagles and the Jets, and on Monday night they crushed the Atlanta Falcons for their fourth straight win. Now the Giants are 4–2, just a game out of first place in the NFC East, and in the midst of the easiest part of their schedule. With a home game against the 2–3 San Francisco 49ers coming up Sunday, followed by their trip to London to play the winless Miami Dolphins, the Giants should be 6–2 when they reach their bye week.

The Giants’ first game after their bye is against the Dallas Cowboys, and there’s every reason to believe that game will be for first place in the NFC East. And as much as Coughlin has been derided during his tenure as the Giants’ head coach, this team’s turnaround has come as a result of playing the kind of football Coughlin has preached since he arrived in 2004: The Giants are running effectively on offense and stopping the run on defense. And if they keep playing that way for the next 10 games, the Giants will still be playing in January.

Although the Giants’ most talked-about defensive performance came when they tied an NFL record by sacking Eagles quarterback Donovan McNabb 12 times, the greatest strength of the Giants’ defense is not its pass rush but its ability to stop the run. A cursory glance at the stats doesn’t show the extent to which the Giants have played solid run defense this season: They rank 11th in the league in rushing yards allowed per game and 14th in yards per carry. But the key to a good run defense is keeping the opposing offense from moving the chains. On that score, Big Blue has an excellent run defense. This season, the Giants have allowed first downs on just 18.1% of the rushing plays they faced, the third best mark in the league.

To keep up that solid run defense for the rest of the season, the Giants need to stay healthy. The middle of the defense — linebacker Antonio Pierce and tackles Barry Cofield and Fred Robbins — is playing very well, but the Giants don’t have much depth. Defensive injuries have plagued the Giants at the end of each of the last two seasons, and they’re not well-equipped to withstand defensive injuries this season.

On offense, the Giants might have the best running back depth in the NFL. Starter Brandon Jacobs is averaging 5.4 yards a carry, backup Derrick Ward played so well when Jacobs missed three games with a knee injury that he ranks ninth in the league with 421 rushing yards, and third-stringer Reuben Droughns is outstanding in short-yardage situations.

The running game has been the most consistent part of the offense, but wide receiver Plaxico Burress has been the most spectacular. Burress has at times been at odds with Coughlin over his practice habits — Burress regularly skips the optional off-season work that most players attend — but this season Burress is showing that he has the talent to perform on Sundays (or Mondays) even when he doesn’t practice during the week. Burress regularly sits out practice to rest his ailing ankle, but so far he hasn’t had to miss any games.

Burress is playing so well this year that were it not for the season Randy Moss is having in New England, Burress would be getting recognition as the best wide receiver in the NFL. Burress and Moss are tied for the league lead with eight touchdown catches, putting them on pace to finish the season with 21, just one shy of Jerry Rice’s NFL record.

Giants quarterback Eli Manning is steadily improving, but he still throws too many interceptions, and if anything derails the Giants’ offense over the rest of the season, that will be it. Manning’s mistakes are especially noticeable when he runs the hurry-up drill: He’s thrown an interception during the last two minutes of the first half in each game of this current four-game winning streak.

If Manning can keep those mistakes in check, the Giants look poised to get to the halfway mark with a 6–2 record. Of course, the Giants started last season slowly, and then rallied to improve their record to 6–2 at the halfway mark, only to finish 8-8 and lose in the first round of the playoffs. This version of the Giants, however, looks more cohesive, more fundamentally sound, and more mature than last year’s team. The Giants are playing Coughlin’s brand of football, and that might mean Coughlin will be around a lot longer than anyone anticipated.

Mr. Smith is a writer for FootballOutsiders.com.