After Monday’s 1-0 win over The Spartans FC in Edinburgh, Neil Critchley’s side were given the opportunity to play at a first-team stadium in a behind closed doors fixture on Thursday.
The hosts took the lead but Jack Bearne levelled with a good finish.
Luis Longstaff was then brought down by the Hearts goalkeeper and Canada international Millar made no mistake from the spot.
Reflecting on the win, U23s boss Neil Critchley told Liverpoolfc.com: “It was great for the boys to play at Tynecastle and it was another good performance.
“We have had a good time in Scotland both on and off the pitch and managed to build up minutes for the players which is the most important thing in pre-season.