The Falcons thought that they had taken the lead late in the opening quarter when Leonard Hankerson was awarded a touchdown from Matt Ryan's pass, but the decision was overturned on review when it was ruled that the ball had not crossed the whitewash.
Atlanta would not have to wait long for the first score, however, going over moments later when Tevin Coleman powered in from a yard out.
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The Giants finally got themselves on the board in the second quarter when Josh Brown kicked a 38-yard field goal, and there was an offensive landmark for quarterback Eli Manning when he went past 40,000 passing yards in the NFL - just the 15th player to do so.
Atalanta restored their seven-point advantage with less than five minutes remaining of the half, however, as Matt Bryant slotted a field goal between the posts from 42 yards.
That lead was wiped out shortly afterwards, though, as Manning combined with Odell Beckham Jr for a 67-yard score to restore parity at the MetLife Stadium.
Beckham's influence on the game was substantial as he began to rack up some impressive numbers, but the Giants were forced to settle for a field goal to give them the lead at the break when Brown kicked over from 44 yards with just seven seconds remaining.