You're confusing total yards with effectiveness. The Giants had only 35 pass plays. The Patriots had 51 pass plays. That's 16 more pass plays to gain 11 more yards. The Giants were more effective passing. Even when adjusted for the interception Eli threw, they still were more effective.
Third, I would argue it's the Giants' ability to run that opened up its passing game. Whereas it was the Patriots inability to run that hurt them when their passing game wasn't working. This appears pretty evident when a team with as prolific a passing game as the Patriots couldn't score more than 14 points against the Giants.
Again, that's a nice theory, but it's not backed up by facts. Look at the last game of the regular season, in which the Patriots' offense scored 38 points. The Patriots rushed for 1.7 yards per attempt (44 total yards), but they averaged 8.0 yards per attempt as Brady went 32-for-42 for 356 yards, two touchdowns and no interceptions. The Patriots actually rushed better in the Super Bowl (2.8 YPC) but were far less effective passing. Obviously, that had nothing to do with their running game.
In the Patriots' two worst rushing games of the regular season that year, against Pittsburgh and Dallas, they averaged 2.4 and 2.6 yards per carry, but they averaged 8.7 and 7.6 yards per pass attempt, put up 34 and 48 offensive points, and Brady passed for 399 and 388 yards, respectively.
Fourth, I find it interesting that you say that the Giants were losing before Eli got lucky. Uh, the Patriots were averaging double digit leads during the season and had a virtual cake walk through the playoffs.
And yet with their vaunted passing game they only had a four point lead versus the Giants.
The Giants played it right. Its defense kept the game close (a defense ranked lower than the Patriots, I might add), used its running game to open up its passing game and won the Super Bowl.
In short, in the game where it mattered most, the team with the better rushing stats won over the team with the better passing stats. Beyond the game itself, the team with the better rushing stats did better than the team with the better passing stats.
Yes, if you have a strong running game it opens up the passing game. But having a better passing game and not a necessarily strong running game doesn't exactly result in ultimate victory. We have the Giants vs. Patriots Super Bowl results as proof.
And, remember, the Patriots had a better ranked defense than the Giants but a superior passing offense than the Giants and yet that passing offense didn't do squat.
Like I said, when the Patriots' passing attack worked as usual, it produced a 16-0 record. The Giants' strong running game produced a 10-6 record in the regular season.
In the Super Bowl, the Patriots' passing game didn't work -- but it had nothing to do their running game working or not working. And the unusual success of the Giants' passing game had nothing to do with their running game working or not working. Before the drive on which the Giants took the lead, the Patriots had been the more effective team passing (although not great, they still had passed better than the Giants, which is why they held the lead). However, from that point on, the Giants averaged 7.6 yards per pass play, and the Patriots averaged minus-2.5. None of that had to do with the running games, because both defenses knew every play would be a pass except one 2-yard carry by Brandon Jacobs in short yardage.
Because they passed successfully, the Giants were able to score the go-ahead touchdown. And because they couldn't pass successfully, the Patriots went backward when they had their chance to tie or win. And as a result of that drive, the Giants finished as the more effective passing team.
