The Scotland cap saved a penalty from Graeme Shinnie just before half-time when the visitors were leading through Andrew Shinnie's 22nd-minute strike.
Killie midfielder Liam Kelly levelled in the 56th minute with a wonderful drive from distance but when the impressive Bell saw red for a foul on last man Ross Draper, it allowed Billy McKay to slam the penalty past substitute keeper Kyle Letheren.
Bell had turned in a terrific performance before his dismissal but the visitors deserved to take the points following a fine afternoon's entertainment.
Both sides went into the game in fine fettle and, unsurprisingly, unchanged from their previous games.
Killie's 2-0 win at Celtic Park last week was their first victory in the east end of Glasgow for a remarkable 57 years.
Caley, meanwhile, won through to the semi-finals of the League Cup with a 3-0 win over Rangers at Ibrox on Wednesday.
Added to the mix was the fact that the last two matches between the sides in Ayrshire had provided fans with 16 goals in total.
The visitors dominated most of the first-half against a strangely subdued Killie side.
Caley threatened first in the fourth minute when Andrew Shinnie cleverly flicked the ball on to supporting midfielder Aaron Doran but his angled drive went just over the juncture of bar and post.
Killie's penalty area then came under pressure as Caley pushed forward with pace and purpose.
When the Rugby Park defence was eventually breached midway through the first-half it was due to some quick-thinking by McKay.
The Caley striker pounced when Doran's shot had been blocked and cleverly flicked the ball back from an acute angle to Shinnie, who had scored at Ibrox in midweek, to slide it low past Bell.
Moments later, poor play by Killie midfielder Rory McKeown gifted McKay another chance but he hesitated going through against Bell and saw his belated shot blocked by the keeper at the expense of another corner which came to nothing.
There was a decent Kilmarnock penalty claim in the 33rd minute when Rory McKenzie raced into the Caley box before going to the ground under a challenge by Gary Warren but referee Euan Norris was unimpressed.
Moments later, McKenzie combined with James Dayton before firing in a drive from the edge of the box which was saved by Antonio Reguero down at his left-hand post.
However, Caley had a chance to double their lead a minute from the break when Norris pointed to the spot after Rugby Park stopper Michael Nelson clumsily body-checked Andrew Shinnie as he slalomed towards goal.
Caley skipper Graeme Shinnie had scored a penalty against Rangers on Wednesday night and he stepped up confidently but Bell made a fine save down at his right-hand post before getting up to make a second clearance.
Kilmarnock came out for the second-half fuelled by a sense of injustice and within a couple of minutes Nelson had headed a Dayton corner over the bar and Sheridan had headed a cross from teenage right-back Mark O'Hara past the post.
However, in the 52nd minute Caley raced up to the other end and Bell foiled McKay again with a good blocking save.
An enthralling encounter continued apace.
Moments later, the impressive McKenzie was fouled 25 yards from goal by Warren but Kelly's free-kick was easily saved by Reguero.
However, in the 56th minute the Killie midfielder, who scored a penalty in the win over Celtic last week was more forceful when he drew his side level with a spectacular drive from 30 yards which flew high past the helpless Reguero.
It was a deserved equaliser for the battling Ayrshire men but on the hour-mark Bell made yet another great save, this time from Andrew Shinnie, who had turned and worked a yard of space for himself in the home penalty area box, before the Killie number one denied the same player seconds later.
There was more drama in the 76th minute when Bell was red-carded by Norris for bringing down Draper after the midfielder had beaten the offside trap and had tried to round the keeper inside the box.
Letheren replaced midfielder Lee Johnson before facing McKay, who slammed the resultant spot-kick into the corner.
There was hardly time to draw breath in a frantic finale.
Reguero made a good save from Killie substitute Paul Heffernan, who had replaced Cillian Sheridan and McKenzie blazed over the bar from the edge of the box.
Substitute Gary Harkins, on for James Dayton, came close with an effort, before Norris brought a remarkable match to an end.
