The pair put on 333, passing Derbyshire’s highest opening stand of 322 between Harry Storer and Joseph Holden against Essex at Derby in 1929.
Reece made a career-best 168 and Godleman was unbeaten on 156 when he declared on 351 for 1 at lunch, setting Northants 326 in 65 overs.
It was clear from the first ball of the morning that an agreement had been reached when Max Holden opened the bowling with his occasional off-spin as Northants donated runs towards an agreed target.
Reece and Godleman, who had played impressively against the front-line bowlers on the third day, passed some notable milestones with Reece becoming only the seventh Derbyshire batsman to score a century on debut against county opposition.
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He passed his previous career-best score of 114 not out and the pair eclipsed the county’s highest first wicket stand against Northants of 273 by Chris Rogers and Wayne Madsen at Northampton in 2010.
Reece was eventually caught off Rob Newton who claimed his maiden first-class wicket as Northants used 10 bowlers in the innings, including wicketkeeper Adam Rossington.