Both teams had a player sent off during a feisty affair with Jake Hyde’s 60th-minute dismissal followed by a late red card for home captain Steve McNulty.
Hyde’s early shower proved the most costly, however, with his team leading 2-0 at the time courtesy of goals from Josh Carson and Emile Sinclair.
A brace by substitute Mark Cullen, though, ensured Luton remain unbeaten at home in the league since September and York are still searching for their first win in 2015.
Carson opened the scoring on 55 minutes when he headed in Michael Coulson’s right-wing cross. The latter was then the provider four minutes later as he pulled the ball back for Sinclair to find Mark Tyler’s bottom right-hand corner from 15 yards.
But, within seconds, Hyde was heading for the tunnel after an over-the-top challenge on Doyle and Cullen reduced the deficit on 65 minutes when he swept in a near-post effort from Shaun Whalley’s corner.
Six minutes later, Luton were level after Cullen headed in from Whalley’s right-wing cross.
McNulty’s 85th-minute red card for a nasty tackle on Brad Halliday then brought a close to an eventful encounter.
York City: Olejnik; McCoy, Lowe, Zubar, Benning; Coulson, Penn, Halliday, Carson (Meikle, 76); Hyde, Sinclair (Fletcher, 75). Unused substitutes: Ilesanmi, McCombe, Montrose, Platt, Ingham.
Luton Town: Tyler; Harriman, McNulty, Wilkinson (Lacey, 52), Howells; Smith, Doyle, Drury (Cullen, 56); Oduwa, Stockley, Hall (Whalley, 64). Unused substitutes: Wall, Justham, Guttridge, Robinson.
Referee: C Breakspear (Surrey).