Scarlets fly-half Rhys Priestland kicked three first-half penalties to put nine points on the board for the home side before Iongi's try made it 14 at the break. Meanwhile, opposite number Stephen Myler responded by kicking a pair of his own to keep it close at half time.
Saints prop Soane Tonga'uiha pulled the road team back to within a point of the Welshmen within five minutes of the restart.
Priestland's fourth penalty of the match put Scarlets back in front after Myler's third had given the road team a brief lead. However, the Saints fly-half soon added two more to his tally to put his team five points ahead.
Fullback Ben Foden crossed the line in the final minutes to extend Northampton's lead, before substitute Ryan Lamb added the exclamation point.