The Slovak beat the Brit for the third time in four career meetings as she sets up a third round match against 15th seed Elise Mertens on Saturday.
Konta, who has had a disappointing 2018, will see her ranking drop all the way down to 43rd as she failed to defend her semifinal points from last year.
Razor-sharp Cibulkova takes first set
Both players started out fairly well on serve with three holds before Cibulkova had the first half-chance, getting to 30-30, but Konta was able to escape trouble with an ace and forehand winner to level the set at 2-2.
There wasn't much between the two and the Slovak was given another chance, this time with a break point, saved by Konta, but given a second opportunity, Cibulkova fired a backhand winner for a 4-2 lead.
The first love hold of the match brought the former Australian Open within one game of the set and she nearly took it on Konta's next service game, but a pair of aces from 30-30 rescued the 22nd seed.
It was only a momentary stay as Cibulkova, serving at nearly 80 percent, closed out the opening set from yet another 30-30 game the Brit spraying a pair of errors as the Slovak captured the opening set in 34 minutes.
Masterful Slovak closes out upset
Again, Konta was under pressure immediately with still another 30-30 game, but she was able to stave off early trouble with some fine serving to hold.
The next service game for the Brit did not see her have the same fortune as, from 40-30 up, she could only watch as Cibulkova blasted three straight forehands to set up break point.
A fourth forehand could only force a weak reply and the Slovak was now in firm control. Playing exquisitely controlled power tennis, winners were flowing from the Cibulkova racket Konta barely able to get a stroke on the ball.
The Brit had whay proved to be her last chance to salvage the match in the sixth game, but a brilliantly played drop shot by Cibulkova saw Konta's volley clip the top of the tape and she escaped further trouble.
Serving to stay in the match, Konta was able to valiantly save four match points, forcing the world number 33 to serve it out. Racing to a 40-0 lead, Cibulkova extracted one final backhand error to complete a sensational victory.
Konta not discouraged despite loss
Although she will sink 19 places in the rankings following her defeat, the Brit is not concerned about her year or level of play so far:
“I actually haven’t regressed. Last year I don’t think I added as much to my game as I would have liked. That hurt me towards the end of the year. This year I feel like I’m heading in the direction I want to be heading in. I think I’m improving. Sooner or later those results will come.
“If they don’t, they don’t. But I’m happy with where I am in my career and with the work I’m doing. I’m clearer on the way I want to play. I think I’m clearer with the shot selection that I want to do.
She pointed to what she has added to her game: “i'm getting fitter. I’m moving forward more, which is something that I’ve always wanted to do.”
Konta doesn't buy into the notion that she could have avoided the Slovak so early had they seeded her over Serena Williams: “She played incredibly well. I wouldn’t say it’s tougher because she would have been seeded. I think it’s just tough because she’s a great player.”
She wasn't happy with Cibulkova's thigh slapping while receiving and let chair umpire John Blom know about it: “I’m trying to focus on my job. I don’t think it’s my job to be pointing these things out. That’s your job.”