A year ago Boro were knocked out of the competition at the first hurdle by Notts County.
Southgate admitted he had learned a lesson from that defeat. While he made changes from the side that played Newcastle United at the weekend, he fielded a strong team against the underdogs.
Former Charlton Athletic defender Luke Young, had the captain's armband for Middlesbrough with George Boateng on the bench.
Former Spurs star Mido was also on the bench.
Northampton were not overawed by the occasion and could even have taken an early lead.
After Dong-Gook Lee had missed an early chance for Boro, Town were desperately unlucky when Ian Henderson struck a post with a diving header.
The opening exchanges were fast and lively with the visitors showing plenty of spirit and determination. Adam Johnson showed flashes of skill on Boro's left-wing.
Home defender Andrew Davies suffered a head injury after 27 minutes. He looked dazed as he left the field for a brief rest in the dressing room.
Davies returned after a seven-minute absence but it was obvious he could not stay on the field. The referee stopped play after a minute and the homegrown product was replaced by Sebastian Hines.
Southgate must have felt a little uneasy early in the second half. Northampton looked to be enjoying the occasion and were eager for a cup upset.
The course of the game changed, however, after 53 minutes when Middlesbrough earned a free kick 35 yards out from goal.
Fabio Rochemback lifted the crowd with a tremendous free-kick that left Mark Bunn helpless.
It was a vital contribution by Middlesbrough's man of the match, who only returned to action last weekend after a three-match ban.
Lee then had the thrill of scoring his first goal for Boro following his move from South Korea last season.
The goal ended any hopes of a Northampton fightback though Henderson was unlucky to see Young clear off the goal-line with Brad Jones beaten.
Southgate introduced former Spurs star Mido in the closing stages and saw him head against the bar.