Mills was given a straight red card by referee Keith Stroud in the 30th minute for a two-footed challenge on David Norris.
And Ipswich wasted little time in taking advantage as headers from Gareth McAuley and Jon Walters put them two goals up at the break.
Reading, who were unbeaten in seven league games prior to this fixture, battled hard after the break and grabbed a late consolation through Gylfi Sigurdsson’s 90th-minute free-kick.
But the hosts held on to move within a point of their opponents in the Championship table.
Roy Keane made one change to his Ipswich line-up, with David Healy starting in place of Shane O’Connor.
Teenage forward Connor Wickham, who turned 17 this week, was among the substitutes following his return from international duty with the England Under-17 squad.
Reading – who were unchanged – received a double boost prior to the game, with Brian McDermott being named as the Coca-Cola Championship manager of the month for March and midfielder Sigurdsson picking up the player of the month award.
Brian Howard saw a shot deflect wide for the visitors early on, while Ipswich’s David Healy forced Adam Federici into action from an acute angle.
Town midfielder Norris was then booked for simulation after going down in the box under a challenge from Zurab Khizanishvili, before Healy threatened again with an overhead kick that forced Federici into further action.
Reading responded with Jobi McAnuff testing Brian Murphy from 25 yards.
But the Royals suffered a setback on the half hour as Mills was dismissed following a strong tackle on Norris.
Alex Pearce was introduced in place of Brynjar Gunnarsson as McDermott looked to reorganise.
However, Ipswich were quick to capitalise on their numerical advantage and took control with two goals in four minutes at the end of the first half.
McAuley opened the scoring with a header from Grant Leadbitter’s corner, after the latter had seen a 30-yard strike tipped away superbly by Federici.
And Reading’s misery was compounded on the stroke of half-time as Daryl Murphy nodded David Wright’s cross back into the six-yard box, where Walters was on hand to apply the finish.
Wickham was introduced at the start of the second half, with Healy the man to make way.
Reading refused to throw in the towel after the interval, although Jimmy Kebe, Shane Long and Brian Howard all failed to test Brian Murphy when presented with chances.
Daryl Murphy sent a curling shot narrowly over and Wright tested Federici from 12 yards as Ipswich looked to put the result beyond doubt.
Wickham, Leadbitter and Jack Colback also brought saves from the Royals goalkeeper as the game drifted towards its conclusion.
Sigurdsson curled home a 25-yard free-kick in the final minute of normal time to set nerves jangling among the home support, but Ipswich were not to be denied.