Granit Xhaka put Arsene Wenger's side in front in the 71st minute with a 25m shot, which Donnarumma could only parry into his own net, and Welbeck finished with a close-range header four minutes from time.
Dortmund drew 0-0 with Red Bull Salzburg, so the Austrian side's 2-1 victory in Germany was enough for them to advance, with Lyon losing 3-2 to CSKA Moscow at home and exiting on away goals.
A large snowstorm on Thursday covered the Russian capital in white just hours before the second leg of the Europa League round of 16 clash between Lokomotiv Moscow and Atletico Madrid was slated to kick off. Temperatures have been rising in recent days and were hovering around 0 degree Celsius (32 F), yet the city woke up completely covered in snow, which obstructed road traffic and is likely to make it hard to play football, reported Efe.
The La Liga outfit took a 3-0 lead to Russian Federation from last week's first leg and showed their class again in the second half at the RZD arena to run out 8-1 winners on aggregate.
Arsenal completed a 5-1 aggregate victory over seven-times European champions AC Milan, winning 3-1 on the night in north London after the Italians had scored first.
Lazio looked vulnerable going into their second leg against Dynamo Kiev after being held 2-2 at home but goals from former Liverpool midfielder Lucas and Stefan de Vrij earned them an impressive 2-0 victory.
He has also won the UEFA Europa League and a UEFA Super Cup in the 2011-12 season, while he reached the final of the Champions League in 2014 but lost to city rivals, Real Madrid.
RB Leipzig knocked out Roberto Mancini's Zenit St Petersburg following a 1-1 draw in Russian Federation.
Sporting Lisbon needed an extra-time goal from Rodrigo Battaglia to overcome Viktoria Plzen.