An undrafted rookie out of Drake, Cundiff is battling Tim Seder, who missed much of last season with a leg injury, for the Cowboys' kicking job.
Cundiff handled all of the kicking duties Saturday night, making two of four attempts. He connected from 46 and 25 yards while missing from 44 late in the second quarter.
Another rookie stood out for the Falcons as fifth-round pick Kurt Kittner trhew a 30-yard touchdown pass to tight end Brian Kozlowski midway through the fourth quarter to give Atlanta a 21-13 lead.
Cowboys rookie Woodrow Dantzler, who went undrafted out of Clemson and is moving from quarterback to wide receiver, returned the ensuing kickoff 97 yards for a touchdown, but the two-point conversion attempt failed.
Atlanta quarterback Michael Vick played into the second quarter and completed three of six passes for 17 yards. Doug Johnson followed and was 14 of 21 for 195 yards with two touchdowns and a pair of interceptions.
Rookie Chad Hutchinson got the start for Dallas and completed all three of his passes for 25 yards.
Quincy Carter, who will start for the Cowboys, came on in the second quarter but left early in the third after taking a shot to the head. He went six of 11 for 70 yards.