Miller stepped up and hit a well struck penalty to the left of goalkeeper Myhre, who although dived the right way, was unable to get to Miller's effort, his 11th goal of the season.
The penalty was enough for Town to take all three points at Portman Road and move up to fourth in Nationwide League Division One completing a perfect Easter for Joe Royle's men, who beat Rotherham 3-1 on Saturday at Millmoor.
Town were without a doubt the best side throughout and looked more likely of the sides to score after the penalty went in, Jim Magilton and Shefki Kuqi all went close for the blues as Sunderland were pegged back.
Marcus Stewart was introduced by Sunderland manager and former Republic of Ireland coach Mick McCarthy around the mid-way mark of the second half, and the former Ipswich Town man recieved a huge welcome from the Town faithful in recognition of his efforts to fire Town to the Premiership and score 21 goald the following season.
Kelvin Davis was rarely troubled in goal in a blues side that kept a rare clean sheet, with Sunderland finding it hard to force a way past experienced duo Matt Elliott and John McGreal at the heart of Town's defence while Ian Westlake's high energy levels meant that Town bossed the midfield for most of the game.
Shefki Kuqi and Darren Bent worked tirelessly upfront and Matt Richards continued his great form since Town's mid-season break in the sun offering both an attacking threat and defending well.
Town head to Gillingham for their next league encounter next Saturday, and with every game now being a big one in the fight for a play off place, Royle's men will be hoping to carry their good run into the game at the Priestfield Stadium to hold on to their fourth place.
Town: Davis, Richards, McGreal, Elliott, Wilnis, Wright, Magilton, Westlake, Miller, Bent, Kuqi (Santos 87). Subs not used: Price, Naylor, Reuser, Bowditch.
Attendance: 26,801.