Ingimarsson crashed home Bobby Convey's free-kick midway threw the first half to secure Coppell victory over his former club and underline Reading's credentials as a Premiership force following two straight away defeats.
Coppell has clearly learned a lot in his ten years since he managed City - and current City boss Stuart Pearce is learning fast too.
Coppell lasted just 33 days in his Maine Road tenure and his three defeats in just six games included a 2-0 reverse at the hands of Reading.
But 24 days into his Premiership run with Reading - and almost three years since he took over the Royals reigns - Coppell is already celebrating victory over his former club.
He is not the most popular of former managers among the City fans, as much for his playing days with the red half of the city as for his brief sojourn as the Blues boss.
Ingimarsson's first-half header hardly improved his standing among the City fans. He converted a pin-point Convey centre after Sylvain Distin had fouled Leroy Lita wide on Reading's right.
The Icelandic star's bravery came at a cost as Distin's desperate attempt to block resulted in a clash of heads which left Ingimarsson dazed and confused, so much so that when referee Webb asked the defender if he was fit to continue, Ingimarsson appeared to ask where his header had ended up.
The answer was in the back of Nicky Weaver's net and Ingimarsson got over his grogginess to force a flying save form the City keeper following Graeme Murty's deflected shot.
City should have equalised soon after Reading's opener only for midfielder Trevor Sinclair to lash widely wide as Ingimarsson dived in to block and Sinclair's frustration boiled over ten minutes into the second half when he was booked for an ugly lunge into the back of Convey's legs.
It got worse for City ten minutes from time when Ousmane Dabo was shown a straight red for leading with his elbow as he challenged Steve Sidwell on the edge of his area.
Reading had already wasted chances to double their lead, James Harper shooting tamely at Weaver with Convey screaming for a pass out wide, then Convey himself dragging a shot wide after Kevin Doyle's blocked effort had fallen kindly for him.
Claudio Reyna had a chance to punish those misses when Ingimarsson flicked a Joey Barton corner into his path, but the midfielder blazed widely over fellow American Marcus Hahnemann's crossbar.
As City pushed for an equaliser, Reading had chances to underline their victory, Doyle hooking over on the turn and City target Sidwell heading over from under the crossbar following a Convey corner.
Weaver produced two fine blocks in the last minute of normal time, first saving with his legs to deny Doyle following a Shane Long drag-back, and then superbly finger-tipping away a long-range effort from substitute Brynjar Gunnarsson.
Then, in second-half stoppage time, Reading were denied a second goal when Doyle rounded Weaver and shot goalwards only for Distin to slide back and clear off the line.