The Blades had snatched the lead in the 52nd minute before keeper Paddy Kenny blundered as Johnson fell over his sprawling arms to win a penalty, coolly tucked away by Mikel Arteta.
United, hoping to bounce back after last week-s 4-0 battering at Anfield, their heaviest defeat of the season, almost found a way through in a scrappy opening period. Stephen Quinn picked out Chris Armstrong who tried to find Jon Stead as Lee Carsley nipped in to clear.
Minutes later the lively Quinn squared the ball to Stead who skipped past a couple of challenges before drilling in a right-foot strike from 15 yards which was scooped up by Tim Howard.
Quinn, in space on the left flank, teased Phil Neville before pumping the ball across the face of the Everton goal with Stead and Rob Hulse unable to add the finishing touch.
Tim Cahill slammed a loose shot high and wide before the Goodison Park outfit almost snatched the lead on 34 minutes, full-back Gary Naysmith's teasing cross from the left was met by Cahill, whose far-post header was cleared off the line by Claude Davis.
Hulse, quiet for most of the half, almost broke the deadlock minutes before the interval, Carsley failed to cut out Phil Jagielka's header and the ex-Leeds man finished with a low drive from the edge of the area saved by the diving Howard.
The Sheffield side went ahead in the 52nd minute with the simplest of goals, Colin Kazim-Richards turned quickly on the edge of the area pumping in a low cross and Hulse beat Joseph Yobo to the ball, sticking out a foot to steer is past Howard from six yards.
Egypt international Ahmed Fathi, signed for £700,000 in January, almost grabbed a second minutes later as he ran on to Stead's precise pass to finish with a shot from 20 yards which flew a fraction wide of the target.
Everton pulled level in the 75th minute after a double blunder by Kenny. Davis slipped up letting in Johnson as the United keeper snatched the ball, but then let it slip through his fingers.
The Everton striker tried to round the stranded keeper but was brought down by Kenny, Arteta smashing his resulting spot-kick against the bar as the ball crashed down a foot over the line.
The Spanish midfielder almost grabbed a second minutes later, United failing to cut out his free-kick from 20 yards, which evaded everyone before hitting the unsighted Kenny on the line.