The result means only goal difference keeps Paul Jewell's side outside the Championship relegation zone, from which Burnley now enjoy a four-point cushion following back-to-back wins.
Before kick-off at Turf Moor, a minute's applause was held to commemorate the life of Gary Speed, and perhaps fittingly it was Wales striker Sam Vokes opened the scoring for the home side.
Vokes, who netted a brace in Speed's final game in charge of the national side - a 4-1 win over Norway earlier this month - got the decisive touch to Keith Treacy's 33rd minute corner.
McCann claimed a last-minute winner when Burnley last beat Ipswich in November 2006, and the midfielder was on hand to double his side's advantage from close range in first-half stoppage time.
His next goal came midway through a second half where Jewell's men displayed scant response - Burnley goalkeeper Lee Grant was a virtual spectator on a bitterly cold Lancashire evening - before Jay Rodriguez made it a 34th birthday to remember for Clarets boss Eddie Howe.
Jimmy Bullard and Lee Bowyer returned to the Ipswich midfield amid four changes from the side that suffered a last-gasp 3-2 loss at home to Reading on Saturday, while Howe recalled Vokes in place of suspended winger Ross Wallace
The game endured a scrappy opening as both sides struggled amid wet and windy conditions, and 16 minutes had passed before either goalkeeper was tested.
McCann disrupted a disjoined passage of play in midfield and found Rodriguez, who unleashed a swerving 30-yard drive that was superbly tipped around the post by the outstretched Arran Lee-Barrett.
Shortly before the half hour Lee-Barrett - selected in place of veteran stopper Richard Wright - produced his second impressive save of the evening, pushing over the bar when Kieran Tripper's measured cross was headed goalward by Rodriguez.
Vokes started that move by intelligently pulling into the midfield, but he was less aware shortly afterwards when Treacy's corner hit the back of his head and went in at the near post.
The goal exposed Ipswich's understandably brittle confidence, and Lee-Barrett parried attempts from Treacy and McCann in quick succession, before Rodriguez dragged wide from 18 yards.
On the stroke of the interval it was 2-0. Junior Stanislas was the architect, leaving Town left-back Aaron Cresswell in his wake before laying on a simple finish for McCann.
It took a magnificent saving tackle from Ipswich youngster Josh Carson, a half-time replacement for Bowyer, to stop Treacy adding a third after Stanislas wrought havoc in the inside-right position once more.
Rodriguez continued in pursuit of his 11th goal of the season, but stabbed wide from a Vokes knockdown and thundered a 20-yard effort narrowly past the post after a surging run.
McCann made sure of the points in the 65th minute as he waltzed unchecked through a chaotic Ipswich defence to chest down Treacy's searching ball and finish emphatically.
The gaps continued to appear in the visitor's backline, and Vokes and Rodriguez passed up close range opportunities before the latter finally claimed the goal his endeavours merited.
When the England Under-21 international collected Stanislas' pass he had only one thing in mind, and a clinical left-foot shot into the bottom corner completed a night of misery for Jewell and co.