Arsenal's victory came without star striker Pierre-Emerick Aubameyang, who confirmed on Thursday that he has been treated in hospital after contracting malaria while on international duty with Gabon.
The 31-year-old scored in Gabon's 3-0 win over DR Congo in Africa Cup of Nations qualification on 25 March.
He played in Arsenal's Europa League quarter-final first leg against Slavia Prague on 8 April but missed Sunday's win over Sheffield United.
"I've spent a few days in hospital this week," he said on Instagram. "I'm already feeling much better every day, thanks to the great doctors that detected and treated the virus so quickly.
"I wasn't really feeling myself the last couple weeks but will be back stronger than ever soon!"
Arsenal produced one of their best performances of the season to turn a potentially difficult night into a fine away victory at Slavia Prague.
With the tie evenly poised at 1-1, they scored three goals in the opening 24 minutes and had another ruled out by the video assistant referee - all-but ending the contest in the opening period.
It kept alive their hopes winning the competition - and with it their only realistic chance of European football next season.
Nicolas Pepe squeezed home at the near post to open the scoring in the 18th minute before Alexandre Lacazette converted a penalty three minutes later following a foul on Bukayo Saka.
Saka coolly swept in the third as Arsenal tore their Czech opponents apart once more, and Arteta's side then controlled the game before Lacazette smashed his second low into the net in the latter stages.
Meanwhile Manchester United eased into the last four of the Europa League after another 2-0 victory over Granada.
The Red Devils' progress was never in doubt after Edinson Cavani provided a smart finish to Paul Pogba's sixth-minute flicked header to extend their aggregate lead to 3-0, after a two-goal win in Spain last week.
United scored a second in stoppage time when Jesus Vallejo turned Alex Telles' cross into his own net.