The visitors showcased their defensive prowess in the second half, securing a well-deserved 2-0 victory and their second consecutive clean sheet of the season.
It is now four games unbeaten for Everton, who remain in 16th place on eight points - but are now five points clear of the relegation zone.
The Tractor Boys had wasted a golden opportunity to take the lead through Jack Clarke but he skied his effort high over the bar and they were also denied a first-half penalty when referee Michael Oliver was called to the VAR screen to reverse his initial decision.
The referee pointed to the penalty spot in the 26th minute when Clarke went down following what appeared to be a challenge by Dwight McNeil but, after being called to the VAR screen, Oliver ruled it out.
TrendingIpswich - who were beaten heavily at West Ham before the international break - remain winless in 17th position after a second home defeat of the season.
Everton have ended a run of 12 successive away Premier League games without a clean sheet, while home and away, the Toffees are just the fourth side to record as many as 20 shutouts in the competition since Sean Dyche's first game in charge in February 2023.
By contrast, Ipswich boss Kieran McKenna revealed this week that defender Axel Tuanzebe faces months out after he was "very close" to losing his thumb in a freak accident at home before the international break.
The fear is that Ipswich could very soon lose grip on their bid to ignite their quest for Premier League safety with their wait for a first win of the season extended to eight games.
Everton, who were without a top-flight victory on the road since at Burnley last December, capitalised on the defensive uncertainty that has been created by Tuanzebe's absence.
Goalkeeper Arijanet Muric is yet to play behind the same back line this season, but he was powerless to prevent Ndiaye giving the Merseysiders a 17th-minute lead when the Senegalese stepped onto a loose touch from Wes Burns to arrow his shot high into the net.
Ipswich were then denied a penalty by VAR.
Everton felt they ought to have had a penalty in their 0-0 draw with Newcastle earlier this month when Dan Burn tangled with Dominic Calvert-Lewin, but they were then the beneficiaries a decision in similar circumstances.
Clarke went to ground as he went to shoot with McNeil in close proximity. Referee Oliver initially felt no attempt had been made to play the ball but VAR Graham Scott advised him to overturn his decision.
Everton maximised their escape by duly doubling their lead and there was nothing controversial about Keane's emphatic finish from an acute angle after good work from McNeil as Ipswich failed to clear a corner.
Ipswich didn't muster a shot on target until the 80th minute as Leif Davis' low corner was met by Conor Chaplin but - in keeping with Ipswich's day - he couldn't connect sweetly with his shot as Jordan Pickford made a routine save.
Calvert-Lewin ought to have added a third with the final kick of the contest after being released by Jack Harrison as Muric saved well, but the wait for a maiden victory of the campaign goes on for Ipswich.