It would still take an astonishing run of results for Harford's men to overcome the huge handicap of a 30-point penalty in League Two, but they have now cut the gap to third-bottom Grimsby to 14 points.
John McCombe put Vale ahead after 26 minutes of Saturday's clash at Vale Park, but the Hatters fought back with goals from Asa Hall, Kevin Gallen and Chris Martin to secure all three points.
Harford said: "You never know in football. We've now got two home games in the next week and the secret is to continue what we are doing.
"This was how I like my teams to play. There were some very good performances all throughout the side and everything came together. We kept the ball when we had to, we hit it long at the right times and we carved Vale open quite a few times. They did have their moments and it needed a great save by Dean Brill to stop us going two down, but overall we certainly deserved to win.
"Getting to Wembley in the Johnstone's Paint Trophy has given us all a boost, but getting results at Port Vale is what football is all about."