Koepka has eyes on the Masters prize on marathon Sunday
Koepka has a four-stroke lead over Rahm but has a marathon day ahead of him with the leading pair still having 30 holes to complete after Saturday's third round was cut short due to rain.
Should the Floridian triumph it will be his first major since the PGA Championship at Bethpage in 2019 and since he left the PGA Tour for the breakaway, Saudi-backed, LIV Golf series.
The prospect of a LIV player putting on the green jacket is an uncomfortable one for the American golf establishment but creates a fascinating subplot to what is so often a day of drama.
The third round will resume Sunday at 8.30am local time (1.30pm BST) with the final 18 holes expected to begin four hours later off the first and 10th tees in pairings.
With puddles forming on the greens and players battling hard against weather more akin to a British Open, organizers had little choice but to end Saturday's action early.
In wet, cold and windy conditions, players huddled under umbrellas in between shots and Tiger Woods wore a woollen hat over the top of his baseball cap.
The weather forecast for Sunday is positive, however, with temperatures expected to rise to above 60 degrees F (15.5 C) and much less chance of rain.
In round three, Rahm and Koepka both made birdies on the par-5 second but bogeys on the par-3 fourth and par-four fifth from the Spaniard left Koepka with his four-shot gap.
Koepka, at 13-under-par, was on the green at the seventh hole with an 11-foot par putt when play was halted while Rahm, on 9-under, had a nine-foot birdie putt.
With the 32-year-old's performances in the LIV Golf League, including last week's win at Orlando, not counting towards the Official World Golf Rankings, he is placed at 118th in the world.
That ranking more reflects the bitter nature of the conflict between LIV and the PGA Tour, who unlike the rebels have places on the board of the rankings body.
Koepka's formal ranking would make him the lowest-ranked player to win the Masters since the rankings system was introduced in 1986.
The current holder of that distinction is Angel Cabrera of Argentina, who was ranked 69th when he won the green jacket in 2009.
The winner on Sunday will collect a Masters record prize of $3.24 million (£2.6m) unless it is amateur Sam Bennett, who plays on the college circuit for Texas A&M.
Bennett will start on Sunday in third place on the leaderboard, having bogeyed the par-5 second, seven strokes off the lead as he bids to become the first amateur to win the Masters.
Tiger makes Masters cut
Patrick Cantlay handled the challenging conditions well as he rose up the leaderboard with three straight birdies from the second hole and he was five-under overall through the 13th hole.
England's Matt Fitzpatrick, the reigning US Open champion, was one of three players level with Cantlay on five under after making three birdies before play was stopped.
Veteran Phil Mickelson, also on the LIV tour, produced a superb long, curling putt on the par-3 sixth for his second birdie of the day to briefly reach six-under but followed that with successive bogeys.
Woods had to battle to avoid the cut but the 15-time major winner may have wished he had failed after a nightmare start to his third round.
Woods, starting on the 10th hole, made two bogeys before double bogeys on the par-5 15th and par-3 16th left him bottom of the leaderboard on six-over overall.
By making the cut, Woods matched the record of Fred Couples and Gary Player with 23 consecutive made cuts at the Masters.
Woods hasn't missed a Masters cut since 1996 when he was playing as an amateur.
