Meanwhile, the Accies remain at the foot of the table but head into this weekend's clash with two games in hand on both Ross County and Kilmarnock, who are precariously placed above them.
Manager Graham Alexander was pleased to see his side record their first clean sheet since he took charge in December and their seventh of the campaign after conceding in all of their previous nine matches.
The Steelmen's fears of relegation have been eased as a run of three wins from their last four games has seen them climb to ninth in the Scottish Premiership, five points above the bottom two with Alexander's men having a game in hand on 11th-placed Ross County.
Motherwell have won only one of their last six top-flight matches against Hamilton and have not scored a league goal against them in over a year.
Securing three points this weekend could move the Steelmen above St Johnstone, who they face next Saturday, and into seventh place.
Hamilton were unable to move off the bottom of the table as their match away at Livingston was postponed on Wednesday night due to heavy snowfall.
The Accies were heading into the midweek clash having secured a precious point against league leaders Rangers after a 95th-minute equaliser from Ross Callachan earned them a hard-fought 1-1 draw.
Hamilton remain at the foot of the table, four points from safety, and they head to Motherwell after failing to score in four of their last six away games, conceding 14 times in the process.
However, the Accies have won three of their last four meetings with the Steelmen, including both of their encounters this season, most recently winning 3-0 in January. Hamilton have also picked up 13 points from a possible 21 available in their last seven league visits to Fir Park.
Victory on Saturday could see Rice's men move above Ross County and one point behind Kilmarnock, who face Rangers this weekend.
Motherwell Scottish Premiership form: DLWWLW
Hamilton Academical Scottish Premiership form: WLDLLD
Motherwell centre-back Declan Gallagher, as well as left-backs Liam Grimshaw (illness) and Nathan McGinley (head), all remain unavailable for selection, while goalkeepers Scott Fox and Trevor Carson continue to recover from their long-term injuries.
Striker David Moyo, who was an unused substitute against Rangers, will be hoping to earn his place back in the starting lineup. However, he will be competing with Bruce Anderson and Andrew Winter for a spot alongside Marios Ogkmpoe in a two-man attack.
Rice could name the same starting lineup that drew with the Gers, which would see the Accies set up with a 3-4-1-2 formation.
Motherwell possible starting lineup:
Kelly; O'Donnell, Mugabi, Lamie, Carroll; Campbell, Crawford, Maguire; Long, Cole, Watt
Hamilton Academical possible starting lineup:
Fulton; Hamilton, A. Martin, Easton; Hodson, Odoffin, Trafford, McMann; Callachan; Anderson, Ogkmpoe
We say: Motherwell 1-1 Hamilton Academical
Both sides performed well in their most recent Scottish Premiership matches and will be hoping to build on their positive results with another strong showing on Saturday.
Motherwell are yet to claim any points against the Accies this campaign but with Alexander's side improving since his appointment, we can see the hosts securing a draw against the league's basement club.