Ipswich came into the match having won ten of 11 games at home this term, the exception being a 0-0 draw with Barnsley, and they were frustrated again as they could find no way through the determined visitors.
Ironically, Ipswich's best chances came when Burnley still had a full complement of players, with Gabor Kiraly denying Alan Lee and Pablo Counago, while Tommy Miller thundered a drive against the bar.
Burnley only threatened sporadically, but they were reduced to hanging on for a point when John Spicer was dismissed for an over-the-top tackle on Jon Walters in first-half stoppage time by ref Phil Dowd.
There were no real complaints about the decision, Burnley's third red card in two matches, and in fact the visitors could also have lost more men.
Graham Alexander was given a stern ticking off after sarcastically applauding Dowd following a first-half booking for dissent, while Robbie Blake escaped any sanction for stamping down on Alex Bruce, also in a tetchy first period.
Ipswich began well and should have scored in the second minute when Danny Haynes floated a cross to the unmarked Lee but the former Burnley man's header was a good height for Kiraly who dived and parried it away.
Kyle Lafferty headed right across the goalmouth for the visitors from Wade Elliott's cross, before Miller was desperately unlucky with a 20-yard thunderbolt which cannoned off the bar with Kiraly helpless.
Lee did some good defensive work to clear a Blake ball which flashed across the face of the home goal before Haynes volleyed well over from a Walters cross.
Kiraly was diving to make a save again on 37 minutes, this time denying Counago when he tried to loop a far-post header in and then the game started to get a little spicy as half-time approached.
A red card looked a possibility, and Mr Dowd obliged when Spicer lunged at Walters, to follow colleagues Joey Gudjonsson and Chris McCann who saw red in last week's 3-2 home loss to Preston.
Ipswich must have felt they would break through in the second half, but in the end they created very little, with Kiraly only forced into a couple of comfortable saves down on his haunches.
Burnley understandably had all bar one back for most of the half, but Ipswich's build-up lacked the pace to find the holes to carve out even a single clear-cut opportunity.
Burnley only had one effort on goal in the whole match, and that was a volley from sub Ade Akinbiyi which went way over with 14 minutes to go.
Despite the introduction of Town's teenage hot prospect Jordan Rhodes for his senior debut and the addition of four minutes of stoppage time, the hosts couldn't find a way through although they did extend their unbeaten home record to 16 matches.