Tiehi scored late into injury time as the Millers were looking down the barrels of defeat.
Matt Taylor's side had taken a surprise lead inside five minutes when summer signing Sam Nombe slotted in his first goal for the club, but a training ground move executed to sheer perfection saw Sam Morsy restore parity shortly afterwards.
A close-range finish from Jack Taylor at the end of a largely insipid second half looked to have settled the game in the Tractor Boys' favour, but Tiehi came up trumps with a stunning strike in the 91st minute to earn Rotherham a well-deserved point.
Had Taylor's goal been the winner, Ipswich would have moved to within a point of Championship leaders Leicester, but a point on the road does see them narrow it to three points with one more game before the November international break. The Millers, meanwhile, move to within four points of safety.
With Ipswich going toe-to-toe with Leicester at the top of the table and Rotherham already battling at the bottom, it looked as though the script was written for this game at the New York Stadium, initially postponed on October 20 after the River Don burst its banks in the midst of Storm Babet.
The Millers, uncharacteristically, pressed high from the off and took a shock lead inside five minutes when Fred Onyedinma seized control of the ball after Davis chested a pass down, drove on and laid the ball on a plate for Nombe to finish.
They were only ahead for 15 minutes, though. Davis shaped up to lift a free-kick from the right-hand side towards the six-yard box, but instead he squared for the unmarked Morsy, who effortlessly passed the ball into the top-left corner.
Town were denied a penalty before the break, too. Odoffin caught Hirst with his right leg in the box, but it seemed as though the theatrics from the latter after the contact made referee Graham Scott's decision for him.
Much of the second half passed without incident, with neither side taking a grip of the game. Spot-kick appeals were again waved away when Axel Tuanzebe's header appeared to strike the hand of Georgie Kelly, who then, at the other end, forced a rare save from Vaclav Hladky after a spot of pinball in the box.
The visitors did eventually take the lead 87 minutes in, when Oliver Rathbone's attempted clearance hit Taylor and bobbled over the line, but resilient Rotherham battled until the end, with Tiehi thundering home after Kelly's blocked shot fell kindly for him.