Howe, 33, was this week unveiled as Brian Laws' successor but the new Clarets manager could not mark his debut with a victory after substitute Chris Iwelumo saw his 66th-minute header hit a post.
Scunthorpe have the worst home record in the Championship, winning just once in front of their own supporters this season, but the result also left Burnley with only one victory on their travels this term.
Howe made two changes to Burnley's starting line-up, with winger Ross Wallace and midfielder Dean Marney both returning to the side.
Former Scunthorpe defender Graham Alexander missed out on a reunion with his former club, and was forced to settle for a place on the bench alongside Iwelumo.
Scunthorpe included new signing Mark Duffy following his signing from Morecambe while midfielder Andrew Hughes was also in the starting line-up after he signed from Leeds on an 18-month deal.
Burnley started the brighter as winger Chris Eagles collected possession in the fourth minute and hit a 35-yard shot which drew a smart stop from Scunthorpe goalkeeper Josh Lillis.
Moments later it was the hosts' turn to threaten as an outswinging corner from Martyn Woolford was met by Sam Togwell's shot from 12 yards.
Clarets defender Daniel Fox cleared the danger but the Iron went close again in the 13th minute.
Togwell was afforded the time and space to fire goalwards from 20 yards and his effort forced Burnley goalkeeper Lee Grant into a fine parried save.
Genuine goalscoring opportunities were scarce and in the 22nd minute Eagles again looked to take matters into his own hands.
He collected possession and thrashed a 35-yard shot narrowly wide of Lillis' right-hand post.
Shortly after the half-hour mark, Scunthorpe striker Chris Dagnall hit a speculative shot from the edge of the area but his effort flew well wide of the mark.
Moments later Eagles joined Jay Rodriguez in a central position, with Wade Elliott taking up a position on the right as the Clarets sought to make the breakthrough.
In the 33rd minute, Burnley created the best chance of the game so far as midfielder Jack Cork created the space for Eagles to fire over the crossbar from 12 yards out.
Scunthorpe were not without a goal threat themselves and Jonathan Forte released Woolford, whose low shot was well saved by Grant.
Burnley were dealt a blow when defender Clarke Carlisle sustained an injury and was replaced at half-time by Andre Bikey.
However, the visitors continued to look more potent in attack and in the 59th minute Wallace narrowly missed the target with a fine strike from 30 yards.
Rodriguez then went close from distance before Howe made a tactical switch, replacing Wallace with Iwelumo in the 62nd minute.
Four minutes later, the Scotland international almost found the net when he connected with a cross from Eagles and headed against the post.
Eagles then curled a 25-yard shot into Lillis' midriff, before Marney headed over from Cork's corner as the Clarets looked to press home their advantage.
Chances came and went in the closing stages but neither side could break the deadlock.