Ten-man Hearts edged out Dundee United on penalties to reach the semi-finals of the Scottish Communities League Cup.
Callum Paterson pounced from close range after 21 minutes to score his third goal for Hearts - all having come on the Tannadice side's home patch.
Johnny Russell poked in an undeserved equaliser 10 minutes from the break.
Darren Barr was sent off after 79 minutes, but Hearts held on to force a shoot-out in which Sean Dillon missed the vital spot kick.
And it is the Edinburgh side who join Celtic, Inverness Caledonian Thistle and St Mirren in next Thursday's semi-final draw.
New United signing Rudi Skacel had to be content with a place on the bench against his former club as manager Peter Houston preferred Richie Ryan as a starter in place of Mark Millar in midfield.
Houston had highlighted the role played by Novikovas in last month's 3-0 league win for Hearts at Tannadice - and that he had altered his formation to deny the winger the amount of space he exploited that day.
However, the Lithuanian was an immediate threat again, sending a 22-yard drive thumping into the boards just wide of the post after John Sutton cleverly chested a long ball into his path.
Hearts manager John McGlynn had signalled his attacking intent by starting Sutton up front with Paterson - Andy Driver being dropped to the bench - and they had United pinned back in their own half.
Their greater fluency finally paid off when Paterson nipped between a clutch of static defenders and Radoslaw Cierzniak to send Ryan Stevenson's driven low cross spinning over the goalkeeper's hip.
Cierzniak had to parry wide Danny Grainger's thundering drive from long-range, while a Mehdi Taouil effort spun past the junction of post and upright, as Hearts threatened to extend their lead.
Russell was starved of service as United's sole front man until he brought his side level after Michael Gardyne's shot on the turn from a Keith Webster cross deflected off defender Andy Webster and the Scotland Under-21 striker poked the ball past goalkeeper Jamie MacDonald.
Although Hearts remained the more fluid outfit, the home side were first to threaten after the break when MacDonald nervously punched clear Gavin Gunning's powerful cross into the path of Stuart Armstrong.
However, the young midfielder failed to test the goalkeeper with a shot that bobbled wide from 14 yards.
Paterson was unfortunate not to extend his tally against United when his overhead kick struck the inside of the post and into the arms of the relieved Cierzniak.
Minutes after being booked for a foul on Willo Flood, Barr was unfortunate to pick up another when he upended Russell after his own hesitation allowed the striker to beat him to a Webster pass.
Skacel replaced Ryan four minutes into extra time to the cheers of both sets of fans and he almost immediately found his new club a goal behind to his old as a Novikovas free-kick flashed just wide.
MacDonald beat away a John Rankin shot and Skacel had the chance to disappoint the fans who idolise him with five minutes remaining but fired wide from 12 yards.
A Rankin 30-yard blockbuster also clipped the outside of the post, but the match was destined to go to penalties.
Grainger and Sutton failed with Hearts' first two spot kicks, but MacDonald saved from Gary Mackay-Steven and Rankin before Dillon stepped up to lash his effort wide.