Keane had accused his squad of lacking character after their defeat to struggling Peterborough in midweek.
But they showed the fight to satisfy their manager and secure a win which lifts them ahead of their opponents and out of the bottom three.
Ipswich were aided by a poor Wednesday performance that will intensify the anxiety around Hillsborough.
Wednesday were without captain Darren Purse, who was sidelined with a hamstring injury, while Etienne Esajas came into the side for Tom Soares.
Keane responded to the defeat to Peterborough with customary ruthlessness.
He made four changes to the starting line-up, with Brian Murphy, David Wright, Shane O'Connor and Edwards all coming in. And it took Edwards just 14 minutes to justify his recall.
The midfielder cut in from the right as defenders backed off, before he rifled a powerful shot across Lee Grant and into the goalkeeper's right-hand corner.
To that point it had been a rather gloomy opening, with Luke Varney's volley, which stung the hands of Brian Murphy on his Ipswich debut, the only real chance.
However the goal ignited the contest.
Marcus Tudgay, who had been wasteful, went close to levelling moments later.
The forward, playing just off Varney, stole a yard in the penalty box and rattled a right-footed shot against the bar.
Tudgay was just as central to another good chance for the hosts soon after.
His neat flick back from Esajas' cross-field ball set up the on-rushing Michael Gray, but goalkeeper Murphy was fast off the mark to smother the midfielder's effort.
Tudgay's eventful few minutes continued as he went down under pressure in the penalty area but the referee was quick to reject his appeals.
With Wednesday edging possession, Ipswich were increasingly confined to counter-attack football, and Daryl Murphy went close with a shot from a tight angle.
But the half ended as poorly it had started, with Esajas slicing a free-kick high into the visiting stand for the hosts.
Ipswich continued to be a threat on the break after half-time with Jack Colback sending Grant sprawling to his right to make a good save.
The visitors went close again seconds later with Damien Delaney heading against the bar from Edwards' cross.
The midfielder was then gifted a great chance as he seized on Esajas' wayward pass and scampered into the penalty area.
But, unlike in the first half, he could not find the bottom right corner.
Esajas was enduring a poor day and was the subject of much of the home fans' scorn.
Wednesday's uncertainty at the back encouraged the visitors, who increasingly pushed the hosts back.
Wednesday, though, could have levelled the game when the ball fell to substitute Leon Clarke at the far post.
But Brian Murphy was again smart to see danger and snuff it out.
The visitors, though, were creating the better chances and thought they had scored a second late on with Jon Walters heading Grant Leadbitter's corner into the net, but the referee ruled it out for a push on the defender.
It did nothing to alter the result, though, as Ipswich closed out the game with relative ease.