Scott Arfield stooped to head home Kieran Trippier's cross with 10 minutes left to seal a ninth win in 10 league and cup matches.
Victory also extended Burnley's lead at the top of the Sky Bet Championship following QPR's draw at Millwall.
"It is all about small margins. They had the better of the first half but we had a solid framework, did the basics and were solid enough not to concede," Dyche said.
"The second half levelled out, although there were pockets of good play. I was thinking it was going to be a 0-0, and then a fine moment of quality saw a good cross and a good header."
There was little to choose between the high-flying Clarets and an Ipswich side that went into the match with their manager, Mick McCarthy, the favourite for the vacant Republic of Ireland job.
Chances were at a premium in a cagey first half which finally burst into life in the final few minutes when Trippier cleared Cole Skuse's half-volley off the line before the Town midfielder whistled a 25-yard shot just wide in injury-time.
The game livened up after the restart with the hosts still on top, in terms of chances created.
Christophe Berra's close-range header lacked the power to beat Tom Heaton while Paul Anderson and top-scorer David McGoldrick both went close from distance without, once again, testing the Burnley goalkeeper.
Ipswich were made to pay with 10 minutes left when the unmarked Arfield stooped to head home Trippier's cross.
Dyche was delighted with Arfield's contribution after deadly front duo Sam Vokes and Danny Ings endured a difficult afternoon.
"I think both pairs of centre-forwards are all very good but defences were on top," he said.
"We had to find a way to overcome that and we did with some very good play."
Ipswich boss McCarthy cut a frustrated figure after Arfield's fourth of the season proved the difference.
"I don't think Burnley were any more accomplished than us, but they had a Johnny-on-the-spot who came in and scored," he said.
"We got what we deserved as they defended their goal better than us for the 90 minutes.
"I was delighted with how we played against a very good side but are they better than us? I don't think so.
"They just have people who are putting the ball in the net and there were three or four tiny little areas which led to their goal.
"We are not that far away. There is not a great deal between us and Burnley."