Rovers continued their preparation for a return to the EFL with narrow 2-1 defeat to Championship outfit Wigan Athletic at Prenton Park on Saturday afternoon.
A Will Grigg penalty and a second half Jamie Walker goal gave the away side the upper hand before Norwood's header two minutes from time got a deserved goal for the Whites.
It did not take long for the away side to make the breakthrough with Grigg converting from the spot after he had been fouled by Manny Monthe.
With Rovers responding well to going a goal behind Micky Mellon's men had a few chances themselves.
After good running by Jonny Smith down the right, Connor Jennings had a chance, but his effort was too high and dipped just after the crossbar.
Another chance for Rovers came soon after and with the home side finding their feet, it was the offside flag which denied Jennings a chance on goal.
Tranmere were not finished there, Zoumana Bakayogo had a chance to finish with a volley from close range after a good cross came in from the right, but his effort sailed over the crossbar.
Another chance came for Tranmere after 20 minutes, with Norwood turned and shot but his effort was well blocked by Dunkley.
At the other end a confident run by Nick Powell took him past two defenders, but good defending by Tranmere cleared the ball with Grigg ready to pull the trigger.
With a few changes at the interval, Rovers came out and picked up where they left off with Norwood smashing his effort against the near post, after finding space in the box.
With chances very, few and far between in the first opening of the second half, the away side had the ball in the net after beating Pilling, but the offside flag was raised.
Rovers with a good attack down the near touchline gave Kai Tonge the chance to level but it was well held by Jamie Jones in the Wigan goal, after some good work by Mullin to work the move.
Tranmere were made to rue the missed chances when the Latics doubled their lead with Jamie Walker finishing off a well-executed move by the visitors.
Wigan had another chance 10 minutes from time to make it three but Vaughan's shot went harmlessly over Paddy Wharton's crossbar, with the teenager not troubled.
Norwood was handed a chance to get something for the home side, but his low effort was parried by Lavercombe in the Wigan goal, with Mullin not quite able to reach out for the rebound.
Rovers finally made their mark on the game towards the end of proceedings with substitute Ben Tollitt working hard to retrieve possession before crossing for Norwood to score, with a downward header into the net.
TRANMERE:25. Pilling (Wharton 75), 3. Bakayogo, 4. Sutton © (McNulty 45), 6. Monthe (Ellis 45), 8. Harris (Banks 45), 10. Norwood, 11. Jennings (Gilmour 61), 14. Caprice (Spellman 75), 15. Norburn (Tonge 61), 18. Smith (Mullin 61), 29. Cole (Tollitt 45)
Unused subs:26. Devine
by Aidan Jones