Koepka, who began the day two shots clear of Rahm with amateur Sam Bennett a further two strokes back, had one birdie through six holes and was staring at an 11-foot par putt at the seventh when play was suspended at 3:15pm ET.
It marked the second consecutive day that rain interrupted play at the year's first major as 39 golfers returned early on Saturday to complete their second round.
Players went out in threesomes off split tees with hopes of completing the entire third round despite the forecast of heavy rain and wind that picked up shortly after the final group headed out with temperatures around eight degrees.
Koepka and Rahm birdied the par-five second hole just as the rain intensified while Bennett made a second consecutive bogey to drop off the pace as the year's first major quickly turned into a two-horse race.
Four-times major winner Koepka moved three clear at the par-three fourth where he got up and down from the left greenside bunker while world number three Rahm made bogey after chipping over the green from the other bunker.
Rahm, who had to finish nine holes of his second round in the rain early on Saturday, fell four shots back after a three-putt bogey from 88 feet at the par-four fifth and was looking at a nine-foot birdie putt at the seventh when play was stopped.
"When we walked up to the seventh green it was clear to us that that green had been wet for a while. They had been squeegeeing it for a while," said Rahm.
"I understand they're trying to push us to play as many holes as possible, but it was very apparent when they tried to get the water out that it just wasn't going to happen in our case."
Players were bundled up as temperatures dropped considerably from earlier in the week and struggled to keep dry while Augusta National's SubAir system that removes water from the course was kicked into overdrive amid the constant downpour.
Bennett was seven shots off the lead while world number four Patrick Cantlay (through 13 holes), reigning US Open champion Matthew Fitzpatrick (11), twice major winner Collin Morikawa (7) and first-round co-leader Viktor Hovland (7) were a further shot adrift in a share of fourth.
Three-time champion Phil Mickelson made an early move with two birdies across his first six holes to move into a share of fourth place, seven back of Koepka, but quickly dropped back with bogeys over his next two holes.
Tiger Woods, who squeaked inside the cut line to tie Gary Player and Fred Couples for most consecutive times playing into the weekend at the Masters (23), was six over par through seven holes and last among the 54 players who made the cut.
Scottie Scheffler, who entered the week looking to become the first player to successfully defend a Masters title since Woods in 2002, was 10 shots back and two under through 12 holes.
Play will resume Sunday at 8:30am ET followed by the final round starting at 12:30pm ET with pairing going off split tees, setting the stage for a marathon day of golf.
"I'm not too concerned about playing 29 holes or however many holes we've got left. It's part of the deal," said Koepka.
"I'm pretty sure I'll be up for it considering it is the Masters. So I don't think anybody should have a problem with that."