Samuel Di Carmine put the home side in front after just three minutes, but Jon Stead equalised and the visitors totally outclassed Rangers after the interval.
Rangers went ahead after Wayne Routledge tricked Ben Thatcher and crossed from the right for Italian striker Di Carmine to score from close range.
Ipswich levelled 11 minutes later, when Stead got in front of defender Matt Connolly to collect David Norris' deflected shot and bundle the ball past keeper Lee Camp.
Stead almost scored again when he charged down a clearance from Camp, who was relieved to see the ball fly over his bar.
Counago headed over from Luciano Civelli's right-wing corner and Stead then missed a great chance to put Town ahead before half-time.
Rangers midfielder Gavin Mahon gifted the ball to Counago, who teed up Stead only for the forward to shoot wide from ten yards out.
Ipswich stepped up a gear in the second half and went ahead in fine style just after the hour mark, when Counago robbed Mahon and went past Kaspars Gorkss before curling the ball into the corner of the net.
It was an excellent strike and the goal that sealed Ipswich's win was arguably even better.
Walters drifted into the area vacated by QPR left-back Damien Delaney - who had just been substituted as Rangers chased an equaliser - and brilliantly controlled Alan Quinn's crossfield ball before firing an unstoppable shot beyond Camp.
Substitute Dexter Blackstock's late header from Lee Cook's cross was comfortably saved by Richard Wright and was the closest Rangers came to pulling a goal back.