Brennan Johnson's first-half brace set Spurs on course for another three points, with the Wales international able to score twice at a ground where his father David Johnson had been prolific across a four-year spell.
Omari Hutchinson pulled one back before half-time and while the relegation-threatened hosts did create other chances, Tottenham made the points safe with late strikes by Djed Spence and Dejan Kulusevski.
An injury crisis across the winter months coupled with a run of six defeats from seven league fixtures sparked some discussion around whether Spurs could become embroiled in a survival battle, but this result moved them 16 points clear of 18th-placed Ipswich and only six off the top half.
"I thought we did the hard things really well," said Postecoglou. "A couple of times in the first half we lost a bit of concentration in terms of the second ball and duels, disappointing goal we conceded, but aside from that I thought we handled that side of the game really well.
"I always felt we were a threat when we had the ball. Sonny (Son Heung-min) was unplayable in the first half and so good to get Brennan back in those areas where he's always a threat.
"All four of our goals were quality goals. We had to do the hard things, but the fruits of that labour was that our front third play was super exciting and clinical.
"We're certainly in a good space of using these two weeks as well as we could to re-energise the team and I think it has.
"We've still got some significant players out. We've got (Dominic) Solanke, Richarlison, (Cristian) Romero, (Micky) Van de Ven, Ben Davies, he's out today. They're all still to come back.
"I just feel like we've got a really good opportunity in these next 10 days to be well equipped for what's ahead.
"What's ahead is obviously Europe but also an opportunity to address our league position, which is obviously not good enough."
Ipswich's defeat combined with 17th-placed Wolves' excellent win at 10-man Bournemouth has opened up a five-point gap to safety.
However, Kieran McKenna insisted they retain optimism and urged his frustrated squad to bounce back on the road at Manchester United on Wednesday.
Asked if he still believed survival was possible, McKenna responded: "Yeah, no doubt and we will while it is possible."
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