Cauley Woodrow scored the winner deep into added time as Luton reached the fifth round of the FA Cup for only the second time in 11 years and add to Everton’s growing sense of injustice. The additional five minutes indicated had passed when a goalmouth scramble followed a corner and Woodrow, a 66th-minute substitute, converted from close range after Arnaut Danjuma’s clearance had rebounded off him. It rescued the Luton goalkeeper, Tim Krul, whose error looked like allowing the hosts to escape with a replay in a tie distinctly lacking in magic for most of the game. Krul let Jack Harrison’s long-range shot squirm from his grasp and trickle over the line to cancel out Vitalii Mykolenko’s contentious first-half own goal. Everton’s back-up goalkeeper João Virgínia, man of the match in their third-round replay victory over Crystal Palace, had kept them in the game with two crucial saves while Nathan Patterson also cleared a shot off the line. Perhaps expectations should have been lowered for a tie between the Premier League’s 17th and 18th-placed teams, both of whom have their focus on avoiding relegation, but Everton failed to make home advantage count with an uninspiring performance and were booed off at half-time. Sean Dyche’s frustration was directed at the lack of VAR intervention for the first goal. Dominic Calvert-Lewin fell to the ground when his loss of balance was aided by a push in the back from the former Everton midfielder Ross Barkley. In the space behind him at the near post, defender Mykolenko diverted Alfie Doughty’s corner past his own goalkeeper. VAR ruled there was not enough in Barkley’s nudge to overturn the goal but Dyche was not happy. “I don’t think I was any more frustrated than I normally am. I was more frustrated with the first goal and two hands in Dominic Calvert-Lewin’s back,” the Everton manager said. “You can say he’s gone down light, which he probably did, but I’ve seen penalties given for treading on someone’s toe.” The Luton manager, Rob Edwards, said avoiding a replay was significant with a home game against Brighton in the league on Tuesday. “It was a big reason for the celebrations at the end,” he said. “It is a competition we value and want to go as far as possible. I’m so pleased for the lads. It will give us belief and confidence, you can see there is belief in this group of players. We are getting better.” Woodrow played on with a suspected broken hand after the Everton centre-back James Tarkowski fell on him but his resilience was rewarded with a first goal since August. “I felt it crack, so I was in a bit of shock for a while,” the forward told BBC Sport. “I’m really pleased with myself because I have been waiting a long time for a goal.”