Rose, in his first round since retaking the world number one spot from American Dustin Johnson on Monday, stumbled to a three-over par 75, his second-worst start in 14 Masters appearance.
"Drove it left the first few holes, hit a couple good putts early that didn't fall, and, yeah, from that point there's nothing really felt easy, I suppose," Rose said.
"Never really found my rhythm." And Casey, who defended his US PGA Valspar Championship crown last month, stood next to last in the field of 87 on 81, with double bogeys at the fifth and 18th holes in a horrow show, his worst of 43 career Masters rounds.
Poulter birdied three of the last six holes to fire a four-under par 68 and share fourth with second-ranked Johnson after 18 holes at the year's first major event.
"My whole game was together, from the first hole to the 18th hole," Poulter said.
"I'm very happy with today's work. It's a great start to a long week."
The 43-year-old Englishman, whose last win came last April in Houston, birdied the par-5 13th and 15th holes and the par-3 16th to finish two strokes adrift of US co-leaders Brooks Koepka and Bryson DeChambeau.
"Just played really steady golf," Poulter said.
"Really my putting all around was extremely solid. I need to do that over the next few days." European Ryder Cup hero Poulter, ranked 32nd, made his best Masters showing in 2015 with a share of sixth.
While Casey appears certain to make an early exit, Rose says he still has a chance to play his way back into contention from nine adrift.
"You want to make the cut, obviously, so get off to a good start. If I can get it back into the red for the tournament tomorrow then you can build a weekend," Rose said.
"I feel I can still get to 11 or 12 under and you never know. I think this golf course offers a Sunday charge and there's a 64 out there, if you can hit the right shots at the right time.
"So I've just got to give myself the opportunity if I do play a dream round, I'm close enough.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)