Polish champions Legia had already done most of the work in the first leg in Wales but carried on attacking to wipe out any lingering doubts with Georgian striker Vladimir Dvalishvili's 53rd minute goal from 10 metres out.
Legia, who reached the European Cup semi-finals in 1970, will next take on Norway's Molde, managed by former Manchester United striker Ole Gunnar Solskjaer.
Bulgarian champions Ludogorets Razgrad overturned a first-leg deficit to reach the third qualifying round by beating Slovan Bratislava 3-0 to win 4-2 on aggregate and give new coach Stoycho Stoev a dream start.
They will face Partizan Belgrade in the next round after the 1966 European Cup runners-up squeezed through on away goals after a goalless draw in Serbia, when they were down to 10 men, gave them a 1-1 aggregate over Armenia's Shirak Gyumri.
Slovenia's Maribor, level with Malta's Birkirkara after a 0-0 first leg, booked a third-round date with APOEL Nicosia with a 2-0 win at home.
Trailing 2-1 from last week's first leg in Slovakia and reeling from Sunday's sacking of coach Ivaylo Petev, Ludogorets made their intentions clear when they took a third-minute lead through Ivan Stoyanov's fine left-footed volley.
The hosts went 2-0 up with 12 minutes on the clock when Dani Abalo finished well after a pass from Junior Caicara. The Bulgarians made sure of progressing with Abalo's second on 78 minutes as the Spaniard produced another neat goal.
It is the first time Ludogrets, who appointed Stoev as their new coach on Monday, will be appearing in the third qualifying round of the competition.
Their next opponents Partizan made hard work of their passage and, although they had seven attempts on target compared to their visitors' single effort, they could not find a way through.
Their cause was hampered in the 55th minute when defender Vladimir Volkov was shown a red card but they held on and went through thanks to the same player's stoppage-time equaliser from the first leg.
In Slovenia, Maribor seized the initiative in their tie with midfielder Goran Cvijanovic's 28th-minute free kick before defender Mitja Viler doubled their lead two minutes into the second half to settle the matter.
The third qualifying round matches are scheduled for July 30 and 31 with the return legs on August 6 and 7.
The winners of those qualifiers will reach the play-off round which offers a route into the lucrative group stage of the continent's elite club competition.
- Sports & Recreation
- Vladimir Dvalishvili
- Stoycho Stoev
- Ludogorets Razgrad