Quarterback Kelly Bryant ran for two touchdowns and Clemson's defense took care of the rest as the third-ranked Tigers held off No. 13 Auburn 14-6.
"I feel like I'm back at Alabama in 1988 after that one," said Swinney, a former player and assistant coach at Alabama. "What a tough, gritty game. That's such a reflection of the heart of our guys.
"You have to find ways to win games, especially early in the season, and I'm just really proud of our guys, particularly on defense."
On a night when defense ruled, Bryant provided Clemson with just enough offensive spark for the Tigers to improve to 2-0 heading into next Saturday's game at No. 17 Louisville.
Bryant completed 19 of 29 passes for 181 yards, but it was his running ability that keyed the victory.
Bryant, who rushed for 68 yards on 19 attempts, scored on a 3-yard run with 48 seconds left in the first half, then scampered 27 yards for Clemson's second touchdown with 11:47 left in the third quarter to provide the Tigers with all the points they would need.
Clemson's defense repeatedly stiffened in the red zone, holding Auburn to zero yards on six plays inside the 10-yard line in the first half and forcing field goals in both instances.
"This was a very disappointing loss," Auburn coach Gus Malzahn said. "We moved the ball well early, but kicking those two field goals and not being able to score a touchdown in the red zone really hurt us."
After surrendering 97 yards to Auburn (1-1) in the first half, Clemson's defense allowed only 20 yards in the final 30 minutes. Clemson, which has led the nation in total tackles for loss each of the past four seasons, had 14 tackles for loss, including 11 sacks -- one shy of the school record.
Junior defensive end Austin Bryant had four sacks, tying the school single-game record shared by Keith Adams and Andre Branch.
"We just needed to help them out," Kelly Bryant said. "We weren't getting into a rhythm offensively, but our defense was out there playing their butts off and we said we had to match the intensity they were bringing out there."
Auburn outgained Clemson 74-6 in the first quarter and Clemson had only 40 yards of offense with four minutes left in the first half, but Clemson struck late to grab a 7-6 halftime lead.
Bryant shrugged off a hard hit that knocked him out of the game for a series midway through the second quarter and guided Clemson 88 yards for the go-ahead score with 48 seconds left in the half, capping the 12-play drive by darting up the middle for a 3-yard touchdown.
Until that score, Auburn held the upper hand for much of the half. Auburn scored on its opening possession of the game, becoming just the second opponent to do that against Clemson in the last 18 games.
Auburn converted three third-downs and one fourth-down in a 15-play, 69-yard drive that ended with Daniel Carlson's 24-yard field goal for a 3-0 lead with 7:13 left in the first quarter.
That lead swelled to 6-0 on the second play of the second quarter as Auburn capitalized on a fumble by Clemson's Ray-Ray McCloud at his own 10-yard line. Auburn settled for another Carlson field goal, this time from 28 yards out, after driving to the Clemson 6.
Auburn running back Kerryon Johnson, who suffered a hamstring injury in last week's season-opening win against Georgia Southern, did not dress out for the game, but starter Kamryn Pettway did and was the Tigers' early workhorse, carrying 16 times for 59 yards in the first half and finishing with 74 yards on 22 carries. Quarterback Jarrett Stidham was pressured much of the night and completed 13 of 24 passes for 79 yards.
"They're defending national champs and their defense is one of the best ones in college football," Malzahn said. "But offensively we just didn't get it done.
"We had too many negative plays. We didn't protect the quarterback when we needed to and we weren't able to effectively run the football. Clemson had a lot to do with that, but we have to find ways to get it done."
Wide receiver Hunter Renfrow led Clemson with nine receptions for 62 yards.