Exeter City and Blackpool will meet at Wembley in the League Two play-off final after a night of high drama in the semi-final second legs. Both sides scored in stoppage time to secure 6-5 aggregate victories over Carlisle United and Luton Town respectively.

Exeter were 2-0 up at St James Park, and 5-3 ahead on aggregate, with 10 minutes remaining thanks to two Ollie Watkins goals, before Carlisle rallied through Jason Kennedy and John O’Sullivan.

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With the tie poised at 5-5 on aggregate, Exeter’s Jack Stacey booked his side’s place in the final with an unstoppable shot into the top corner from 25 yards in the last minute of stoppage time. Exeter will now face Blackpool at Wembley on 28 May, with Paul Tisdale reminding his players the job is only half done.

“I have been here before with Exeter, I have been in two finals, won one and lost one, so I know what it feels like to win and what it feels like to lose,” Tisdale said.

The Carlisle manager, Keith Curle, said: “We walk out of the stadium with our head held high. They have given me everything, of course there is an element of disappointment. But what we don’t do is we don’t sulk out of here, we have improved since I have been at the football club and there is a winning mentality that we need to maintain.”

In the other semi-final, the Luton goalkeeper Stuart Moore scored a 90th-minute own goal at Kenilworth Road to send Blackpool through.

Facebook Twitter Pinterest Luton goalkeeper Stuart Moore is inconsolable after his last-gasp own goal handed Blackpool a place in the play-off final. Photograph: Pete Norton/Getty Images

Nathan Delfouneso opened the scoring for Blackpool before a Kelvin Mellor own goal and a Scott Cuthbert header brought Luton level on aggregate. Danny Hylton scored a highly contentious penalty to put the hosts ahead before Armand Gnanduillet’s header made it 3-2.

With extra time looming, Jordan Cook’s attempted clearance rebounded back off the luckless Moore and into the net to make it 3-3 and secure Blackpool’s Wembley date.