The games required less than 20 minutes to produce an incredible moment as Christian Eriksen fired Denmark into the lead three years after he suffered a cardiac arrest in his country's opening game at the Euro 2020.
Eriksen ran onto Jonas Wind's fine pass before producing a clinical finish to get his country off to a dream start at the MHP Arena.
The Danes continued to control the contest and should have extended their advantage when Rasmus Hojlund was denied from close range just after the hour mark.
Their inability to find a second goal ultimately proved costly as Janza scored the all-important equaliser in the 77th minute to become just the third Slovenia player to score at the European Championships.
With neither side able to find a late winner, Slovenia celebrated their 24-year wait for European Championship football with a precious point.
Eriksen produces memorable Euro 2024 moment
Denmark may have made the stronger start but it was Slovenia who unleashed the first shot in anger in the 16th minute.
Sesko, who recently committed his future to RB Leipzig, opted to try his luck from distance, fizzing a powerful effort just past the post to showcase the sort of confidence that saw him net 18 goals in his first season in Germany.
However, Slovenia's moment of promise was forgotten less than 60 seconds later as a piece of lapse defending from a throw-in allowed Denmark to open the scoring.
Wolfsburg's Wind produced a neat flicked pass from the throw-in, turning the ball into Eriksen's path, before the 32-year-old chested it down to steer a composed right-foot strike into the bottom corner.
After scoring his second goal at a major tournament, Eriksen was presented with the chance to grab a third in the closing stages of a dominant first period for the Danes.
The Man United man was once again teed up by Wind, but on this occasion, he could only blaze his wayward effort into the Denmark contingent behind Jan Oblak's goal.
Slovenia battle back to clinch point on European Championship return
Kasper Hjulmand's side continued to control proceedings after the half-time whistle, and their control looked set to yield a second goal when Victor Kristiansen picked out Hojlund with a low cross, only for Oblak to make a superb save from point-blank range.
From nearly doubling their advantage, Denmark could easily have conceded a leveller just a few moments later.
Andraz Sporar's lofted cross was perfectly weighted for Adam Gnezda Cerin to attack, but his headed effort went harmlessly wide to the relief of experienced Denmark goalkeeper Kasper Schmeichel.
Sporar was the next man to spurn a promising opportunity, steering his shot just wide after meeting a whipped free-kick.
Matjaz Kek's side continued to pile on the pressure and continued to experience frustration as Sesko sent a deflected long-range effort crashing against the upright.
Their mood quickly changed when the resulting corner broke to left-back Janza, whose fierce first-time shot deflected off Morten Hjulmand and past a helpless Schmeichel.
Slovenia looked the likeliest to go on and grab the winner, but a failure to snatch all three points could not detract from the fact that this was a valuable result for a side that were making just their second appearance at the European Championships as an independent nation.
What next for Slovenia and Denmark?
Having picked up a valuable point, Slovenia will now attempt to claim their first-ever win at the European Championship when they face Serbia on Thursday.
While Slovenia will travel to Munich, Denmark will head to Frankfurt for a clash with England in a rematch of the Euro 2020 semi-final at Wembley.