The result means the Blades have a six-point advantage over third-placed Leeds United, which hosts Aston Villa at Elland Road in its game in hand on Monday (AEST).
Scott Hogan turned home Jack O'Connell's cross in the 24th minute to put the Blades on course for victory at Bramall Lane, although they had to be patient in their pursuit of a second goal.
Oliver Norwood's free-kick was kept out by the post, while David McGoldrick and John Egan spurned headed opportunities after the interval.
However, United's dominance saw Ipswich's resistance eventually broken in the 71st minute, O'Connell nodding in John Fleck's corner from close range.
Leeds needs to win both its remaining Championship fixtures and United to slip up on the final day at Stoke City to finish above its Yorkshire rival, although Chris Wilder's side also has the added cushion of a far superior goal difference.