The Seasiders were the first team through, despite losing 3-2 in Lithuania, going through on away goals.
Atlantas took a 12th-minute lead through a penalty from Dainius Zernys, who was sent off three minutes later, but Greg Stones hit back with a header on the half-hour.
Gary Powell put Rhyl ahead on the night, but Aivaras Laurišas and Andrius Peterikis set up a nail-biting finish.
The match ended amid ugly scenes as Atlantas manager Igoris Pankratjevas raced onto the pitch and clashed with Alan Morgan and goalkeeper Gerald McGuigan at the final whistle.
Meanwhile Carmarthen mauled Eircom Leaguers Longford Town in the second half of their game as they secured a 5-1 victory.
Despite opening a 16th minute lead through Danny Thomas, their hopes looked to have been dashed four minutes later when keeper Tony Pennock brought down Andy Myler, who converted the resulting penalty.
But Carmarthen silenced a boisterous Irish support after the interval and hit the Irishmen with a four-goal second half blitz.
Gary Lloyd struck twice, - his second a penalty - before Thomas added his second.
Nathan Cotterall sealed the victory 10 minutes from time when he took advantage of a goalkeeping blunder outside the box to put the ball into an empty net.
The two Welsh Premier League sides join former WPL giants Barry Town as the only Welsh Premier clubs to win a European tie.