Snodgrass' goal was not enough to earn his side all three points at Elland Road but the result kept them a point above the Bluebirds in the table.
The Scotland winger touched in from close range with 18 minutes left to finally beat compatriot David Marshall, who had produced a string of excellent saves to preserve a lead given to his side by Joe Mason.
The striker capitalised on a Darren O'Dea error to score his third goal in as many games with 17 minutes gone, and Marshall then took over as Cardiff looked set to continue a hoodoo they have held over Leeds since 2005.
But, despite keeping out Snodgrass, Ross McCormack, Adam Clayton and Jonny Howson with some memorable stops, Marshall could do nothing when Snodgrass got free in the box to win his side a point that could have been more on another day.
With the sides having scored 47 goals between them before kick-off, a high-octane start was always likely and so it proved.
Much has been made of the high-profile errors made by Paul Rachubka since he replaced the injured Andy Lonergan in the Leeds goal a fortnight ago, but he proved his worth early on, getting down low to turn a goal-bound strike from Aron Gunnarsson around the post.
Leeds then clicked into gear and Tom Lees had a header blocked in a busy box, before Andy Keogh - a former Cardiff loanee - worked Marshall with a header.
But while both sides know their way to goal, they had also conceded a combined tally of 39 going into the game and that became 40 when Cardiff took the lead after a mistake from O'Dea.
Although heading towards his own goal, the Republic of Ireland defender was winning a foot race with Mason all the way but hesitated over clearing the ball and, despite a suggestion he was given the slightest of shoves, he was promptly pick-pocketed by the lively 20-year-old who duly rounded Rachubka and slotted in.
No strangers to having to come from behind Leeds quickly looked for a way back, with Snodgrass forcing Marshall to turn his header around the post as he followed up a Keogh flick, before Danny Pugh's volley was blocked behind.
O'Dea was then withdrawn, capping a disastrous opening 30 minutes for the Celtic loanee, although there were suggestions as he left the pitch that he was struggling with his vision.
The same could have been said of City defender Mark Hudson when he somehow failed to get on the end of Craig Conway's brilliant free-kick, although he did his job at his own end of the field as half-time approached, putting his body on the line to keep out what would surely have been Howson's first of the season.
Snodgrass, always Leeds' greatest threat, looked to spark his side after the interval with a venomous 25-yarder that Marshall beat away, with the impressive keeper then going full stretch to keep out McCormack.
The heroics continued to come from Marshall, with Clayton's 25-yard piledriver destined for the back of the net until he somehow got a touch to it, before, after another Clayton strike was blocked behind, he produced a stunning one-handed stop to keep out a Howson header.
Eventually, though, Leeds found a way past him when Snodgrass levelled in the 72nd minute. Patrick Kisnorbo sent a free-kick into the box, Lees flicked it on and Snodgrass got a run on his marker to beat Marshall - who still got a hand on his prod - from two yards.
The wave of home possession continued after the goal and Lees should have done better than glance a cross from substitute Lloyd Sam wide, before Cardiff created the final chance of the game, with Aidy White clearing from under his own bar as Gunnarsson looked to pounce.