Cole Skuse went close with two late strikes but Town and Burnley are level at 0-0 at the break.
Mick McCarthy named the expected unchanged line-up for the fifth game running with the only switch of personnel in the matchday 18 Jack Marriott coming on to the bench in place of Anthony Wordsworth. Championship leaders Burnley were also unchanged.
Clever work on the left from David McGoldrick conjured the first opportunity in the fifth minute. The striker found space for Ryan Tunnicliffe on the left and eventually received the ball back from Daryl Murphy inside the area, but ex-Canary Jason Shackell got across to block as the Blues’ top scorer looked to shoot.
Town had the better of the early stages of a game played on a wet surface with drizzle continuing to fall. Burnley’s only significant foray forward had been an early break down the left from Michael Kightly but his cross was easily cut out by Cresswell.
The Blues continued to have most of the ball but without threatening. At the other end, Dean Gerken had little trouble with Scott Arfield’s weak 22nd minute effort, then Christophe Berra did well to take the ball away from Danny Ings as the striker looked to take it down and past him on the edge of the area.
On 28 Hyam won the ball midway inside the Clarets’ half, Cresswell eventually crossing into the box where it fell to McGoldrick eight yards out. The striker tried to find space to shoot but could only scuff an effort goalwards which was cleared. At the other end, Sam Vokes shot high and wide from a tight angle but having strayed offside.
Burnley right-back Kieran Trippier did superbly to reach a David Jones ball down the right in the 31st minute, his low ball flashing across the area.
Blues keeper Gerken suffered what appeared to be a knee injury in that incident as he and Vokes collided and, having received treatment on a couple of occasions, was eventually forced off, Scott Loach taking over in goal and making his first appearance since the Leeds defeat in August.
On 40 Kightly intercepted from Berra on the Burnley left but his low cross was cut out by Luke Chambers. Two minutes later, Paul Anderson headed past the post from a wayward Burnley clearance.
Just before the break Cole Skuse twice came close to opening his Town goals account. First he slammed a loose ball inside the area into Trippier's face inside the six-yard box, then Tunnicliffe teed him up 20 yards out and his strike flew narrowly past Tom Heaton’s left post.
Town just about had the better of the first half, although without having tested Heaton significantly.
At the other end, the Blues backline had largely managed to nullify the threat presented by 19-goal strike pair Vokes and Ings, with Kightly, who was plucked from non-league Grays Athletic by Mick McCarthy during his Wolves days, the main threat down the left.
Town: Gerken (Loach 39), Chambers, Berra, Smith, Cresswell, Anderson, Hyam, Skuse, Tunnicliffe, Murphy, McGoldrick. Subs: Hewitt, Mings, Tabb, Edwards, Nouble, Marriott.
Burnley: Heaton, Trippier, Duff, Shackell, Mee, Marney, Vokes, Ings, Jones, Kightly, Arfield. Subs: Cisak, Lafferty, Stanislas, Edgar, Treacy, Long. Referee: Graham Scott (Oxfordshire). Att: