It was a stop-and-go night for Holbrook, who completed 23 of 33 attempts for 280 yards passing. But he had three interceptions through the first snap of the second quarter after throwing nine total last season.
New Mexico State got a big lift from its defense, which kept Southeastern's offense out of the end zone until the closing minutes.
Holbrook, who set NCAA records for a sophomore, eventually found his rhythm.
With the Aggies ahead 21-7 in the third, Holbrook threw a 7-yard scoring strike to Derek Dubois and found Brandon Allen on a 57-yard scoring play. Both TDs came over a three-minute span late in the period.
It was a contrast from Holbrook's shaky start. Southeastern's Demerious Johnson returned the first interception 30 yards for a first-quarter touchdown and Eric Jackson added two more picks.
The Aggies took the lead for good at 14-7 in the second quarter when the 273-pound McKinney intercepted Southeastern quarterback Brian Babin, rumbled 68 yards and dropped into the end zone.
Holbrook then added a 98-yard drive to put New Mexico State up 21-7 at halftime after a 13-yard scoring pass to Chris Williams.
The Aggies were pinned deep to start that series after a great punt by Cody Samples. Facing third-and-7 at the 5-yard line, Holbrook completed a 21-yard pass to tight end Nick Cleaver.
Dremel Adams broke free on a 62-yard TD run with 2:07 remaining, pulling Southeastern to 35-14.