Both sides finished with 10 men as an incident-packed match finished level.
A David Kee shot and Mark Haughey header had the Blues two up at the break but Martin Donnelly and Caoimhin Bonner brought the Reds level.
Linfield's Sean Ward was sent-off for bundling Chris Curran over but George McMullan saw the penalty saved.
McMullan put Cliftonville 3-2 up with a superb chip and sub Aaron Burns headed Linfield level before Eamonn Seydak was dismissed for two yellow cards.
After the match, it emerged that Cliftonville defender Bonner was shown a red card following clashes in the tunnel area as the teams left the pitch after the final whistle.
The result means Linfield's lead at the top of the table has been cut to two points by second-placed Crusaders who won 4-2 away to Ballymena United.
The big turning point
Linfield looked to be in total command when they led 2-0 at half-time.
They had a great chance to go three up but top scorer Andrew Waterworth pulled a low shot wide from a great position early in the second half.
That proved crucial as, five minutes later, the sides were level through Donnelly and Bonner.
McMullan's spot-kick was then well saved by Ross Glendinning but the Blues keeper was beaten soon afterwards by the home skipper's audacious chip.
What they said
Linfield manager Warren Feeney: "It feels a bit like a defeat as we were 2-0 up.
"At half-time I thought it was one of our best performances but I knew Cliftonville would come back at us.
"Andrew Waterworth had a great chance to go 3-0 up - but those are the fine margins in football."
- Cliftonville have lost just one of their last 13 league matches against Linfield
- Linfield's Andrew Waterworth has 15 goals this season but has still to score in an away league fixture