Idris Kanu came close in the 15th minute with a curling effort that drifted narrowly wide. He tried again four minutes later after beating three defenders, but his effort sailed over the crossbar.

Approaching the half-hour mark, Romoney Crichlow’s powerful low drive beat goalkeeper Luke McGee, but Olly Scott cleared off the line.

Tranmere started the second half brightly, with Tom Ince’s free-kick blocked, while Scott fired narrowly wide of the top-right corner.

Barnet goalkeeper Matthew Cox was called into action on the hour mark, producing an acrobatic save to deny Charlie Whitaker at the near post.

Five minutes later, Cox denied Whitaker again, with the rebound striking the woodwork.

Barnet broke the deadlock in the closing stages when Brandon Comley’s cross from a well-worked corner found Smith unmarked, and he smashed the ball into the roof of the net.

Ofoborh doubled the lead in stoppage time, meeting Ajayi’s pass and slotting home with his left foot. Ajayi then completed the scoring with a fine finish to send the Bees into the second round.