Results at Falkirk and Inverness - greeted with jubilation at the final whistle - leave those two sides facing a final-day battle to beat the drop, while Billy Reid's team, promoted last season, stay up.
David Clarkson opened the scoring midway through the first half, slotting home after Cillian Sheridan's counter-attacking effort was blocked.
Sheridan scored the second just before the hour and striking substitute John Sutton rounded off the win by netting five minutes from time.
Accies manager Billy Reid welcomed midfielder James McArthur back from suspension as of four changes to his side, while Motherwell made three alterations, including drafting in fit-again captain Stephen Craigan.
Ipswich boss Roy Keane and several Premier League scouts were in attendance at New Douglas Park to watch the performance of Accies' highly-rated teenage midfielder James McCarthy.
He helped set up the first chance of the game on three minutes, but Derek Lyle mishit the eventual shot from his cross well wide of the near post.
McArthur went close minutes later after a pass from Joel Thomas, but after cutting inside, the midfielder saw his acute-angled shot cleared off the line by Craigan.
Motherwell earned a free-kick outside the left side of the box after good work by Clarkson and Stephen Hughes, but Jim O'Brien's set piece was headed clear, and Maros Klimpl and Sheridan both tried their luck with distance drives which failed to trouble Tomas Cerny.
Motherwell took the lead with a blistering counter-attack at the midway stage of the first half after goalkeeper Graeme Smith had punched clear a Lyle free-kick and McArthur's attempt from the rebound.
Sheridan blasted his way to the byline at the opposite end and although Cerny blocked his initial shot from beside the left-hand post, the striker coolly played it back to Clarkson, who swept home from six yards.
Hamilton continually pressed for an equaliser and only a good diving block by Smith repelled Mark McLaughlin's close-range volley from a Lyle free-kick, while Chris Swailes' header from Brian Easton's corner was just kept out at the left-hand post.
Alex Neil then orchestrated a good period of possession on the right, but Lyle was unable to connect with Martin Canning's cross; and Shaun Hutchinson scrambled to clear off the line when Lyle sent in a dangerous shot in injury-time.
Motherwell were first to threaten after the break but Accies tried to find their equaliser when Neil lofted the ball over the defence to the byline, only to find Thomas unable to control it.
The hosts withdrew defender Swailes after 52 minutes to introduce forward Kenny Deuchar, while Thomas blasted over the bar after linking with Simon Mensing on the right.
However, it was Motherwell who doubled their lead shortly before the hour; the home goalkeeper and defence failed to deal with a Hughes cross and it broke to Sheridan, who slotted it home from an acute angle beside the right-hand post.
McLaughlin then fired over the bar, while Canning's header from an inswinging Lyle corner to the far post was punched away and Mensing tried a dipping shot from an Easton cross, but fired wide.
Motherwell substitute Steven McGarry was set up for a shot by some good footwork on the left by O'Brien, but his strike was easily blocked.
Stuart Taylor had an effort for Hamilton within a minute of being introduced as a substitute by the home side in place of McArthur, but although Accies hustled and harried around the penalty box, they never troubled Smith in the closing stages or threatened to salvage what would have been a vital result.
Paul McGowan saw his stretched effort slide narrowly wide and from Lyle's corner, the ball hitting off three home players' feet as it rolled agonisingly across the face of goal.
Instead, it was Motherwell who made it 3-0 five minutes from time.
Sheridan reached the byline and cut the ball back through a crowded box for Sutton, who lashed home from close range eight minutes after coming on.