It was a dream start for caretaker-manager Neil Redfearn on Saturday as the Whites claimed their first Championship win on the road in five matches.
Redfearn, who has refused to rule himself out of the running for the job on a permanent basis after Simon Grayson was sacked on Wednesday, made a winning start to life as temporary boss thanks to Snodgrass' 12th of the season at the end of the first half, McCormack's 15th in the 79th minute and a late Becchio strike.
But Redfearn and Leeds were given a big helping hand by City pair James Wilson and Yannick Bolasie, who were both sent off by referee James Linington.
Defender Wilson was shown a straight red card for a professional foul after bringing down McCormack in the 44th minute and the home side were reduced to nine men when winger Bolasie was booked twice in three minutes early in the second period.
Former Leeds midfielder Neil Kilkenny was back in City's starting line-up against his former club, while defenders Liam Fontaine and Wilson were also recalled to the side.
Danny Pugh replaced Andros Townsend on the left side of midfield for Leeds and new loan signing Adam Smith made his debut in the back four following his deadline-day arrival from Tottenham.
City began to look the more impressive side after a scrappy opening. Bolasie forced Leeds goalkeeper Andy Lonergan into a full-length save with a shot from outside the area and Kilkenny was also on target with a thumping drive that was well held.
City were the dominant side but created little and save for Albert Adomah's angled drive, which was brilliantly turned away by Lonergan in the 38th minute, had nothing to show for their efforts.
Leeds then took the lead against the run of play with their first meaningful attack.
A swift break involving Becchio, Pugh and McCormack set up Snodgrass on the edge of the area and his low shot wrong-footed City goalkeeper David James.
The home side were then reduced to 10 men just before the interval. Wilson gave chase after McCormack had darted clear on goal and after hauling down the Scottish striker, the City defender was dismissed.
City manager Derek McInnes sacrificed playmaker Kilkenny in order to send on Ryan McGivern, another defender, at half-time.
But McInnes' plans were in disarray within 12 minutes of the second half following the sending-off of Bolasie.
Having just been booked for his foul on Leeds debutant Smith, the Congolese was shown a second yellow card for another poor challenge on the same player and City's uphill task suddenly became mountainous.
Leeds moved the ball from one side of the pitch to the other to stretch City's nine men and after creating numerous chances made the game safe with a second goal in the 79th minute.
Midfielder Adam Clayton clipped a fine ball over the City defence into the path of McCormack, who lashed home a low angled shot inside the far post from the edge of the area, and Becchio completed the scoring by firing home Aidan White's cross in stoppage time.