Sunderland had taken a 10th-minute lead through on-loan Liverpool striker Fabio Borini and a fine first-half display left them on course for a first piece of major silverware since 1973.
However, City responded in the second half, with Toure lobbing in a superb long-range equaliser and Nasri smashing home less than two minutes later before substitute Jesus Navas added a third goal at the death.
“The team deserve this cup because we played well during the whole cup and scored a lot of goals,” said City manager Manuel Pellegrini.
“Sunderland played a good match also and we didn’t move the ball as fast as we needed (in the first half), but in the second half we scored two beautiful goals and had the patience to wait for the moment.”
Victory for City enabled them to partially atone for the shock of last season’s loss to Wigan Athletic in the FA Cup final and sets them up for a tilt at a domestic treble.
City are six points off the pace in the Premier League with two games in hand and will face Wigan in the FA Cup quarter-finals, while they also trail Barcelona 2-0 in their Champions League last 16 tie.
It was a bittersweet first trip to the new Wembley for Sunderland but they could reflect with pride on a valiant display that augurs well for their Premier League relegation battle and forthcoming FA Cup quarter-final against Hull City.
“We did everything we could,” said Sunderland manager Gus Poyet.
“That’s the best part of what we are all about. To beat us they had to score two wonder goals. I hate losing but I’m proud of the players.”
City welcomed back top scorer Sergio Aguero after a month out with a hamstring injury and he served an early reminder of his threat with a snapshot that was parried by Sunderland goalkeeper Vito Mannone.
Sunderland had started the game with intent, however, snapping into tackles in the middle of the pitch, and a minute later they rocked City by taking the lead.
Lee Cattermole, starting in place of the cup-tied Liam Bridcutt, robbed Toure just outside the Sunderland area and fed Adam Johnson, who lofted a ball down the right flank for Borini to chase.
Vincent Kompany got to the ball first but the City captain’s attempted clearance was blocked by Borini, who cut into the box from the right and deftly found the bottom-left corner with the outside of his right foot.
Sunderland were quick to gather men behind the ball afterwards but they continued to threaten, with Wes Brown heading over from a corner.
When City did muster an attack, Nasri saw a tame shot saved by Mannone and it took a magnificent last-ditch block by Kompany to prevent Borini from extending Sunderland’s lead before half-time.
It was to prove a spurned opportunity that Sunderland would rue, as within 11 minutes of the restart, City were in front.
The teams exchanged chances early in the second half, David Silva testing Mannone and Costel Pantilimon pushing a long-range Ki Sung-yueng effort over at the other end, before Toure equalised with an exquisite strike.
With Sunderland camped inside their area, Pablo Zabaleta rolled the ball back to Toure and the giant Ivorian lifted a gloriously nonchalant effort over Mannone and into the top-left corner from 30 yards.
Sunderland barely had time to draw breath before Nasri made it 2-0 in the 56th minute, meeting Aleksandar Kolarov’s deflected left-wing cross with an emphatic shot from the edge of the box that swerved deliciously inside the left-hand post.
Immediately, City introduced Navas in place of Aguero, while a shellshocked Sunderland sent on Craig Gardner and Steven Fletcher, who quickly tested Pantilimon with a low shot.
Kompany almost added a third for City when he hooked wide from a Nasri corner, before Navas rattled a shot inside Mannone’s near post from Toure’s pass to rubberstamp City’s third League Cup crown.