The BMC rider was one of four who raced away on a bitterly cold stage shortened to 136.5km owing to snow at the start.
Ben Swift, formerly of Team Sky and now riding with UAE Team Emirates, was the highest-placed Briton in fifth.
Fabio Felline kept the overall lead, while Chris Froome finished 77th to remain 29 seconds off the pace.
Alex Dowsett of Movistar, who also finished among the main bunch in 48th, described conditions as "very unpleasant", while 24-year-old Quick-Step rider Bob Jungels tweeted it was "the coldest day on a bike so far for me".
The six-day, five-stage race in Switzerland is an early indicator of form before July's Tour de France, which Team Sky rider Froome will be bidding to win for a fourth time - and the third in succession.
Friday's third stage is a 187km ride starting and finishing in Payerne that includes four category-three climbs.
Tour de Romandie stage two result:
1. Stefan Kung (Swi/BMC) 3hrs 33mins 15secs
2. Andriy Grivko (Ukr/Astana) Same time
3. Sonny Colbrelli (Ita/Bahrain) +20secs
4. Alexander Edmondson (Aus/Orica) Same time
5. Ben Swift (GB/UAE Team Emirates)
6. Fabio Felline (Ita/Trek)
7. Tosh Van der Sande (Bel/Lotto)
8. Jarlinson Pantano (Col/Trek)
9. Diego Ulissi (Ita/UAE Team Emirates)
10. Maximiliano Richeze (Arg/Quick-Step)
Overall classification after stage two:
1.  Fabio Felline (Ita/Trek) 8hrs 12mins 42secs
2.  Maximilian Schachmann (Ger/Quick-Step) +8secs
3.  Jesus Herrada (Spa/Movistar) Same time
4.  Primoz Roglic (Svn/LottoNL) +9secs
5.  Ion Izagirre (Spa/Bahrain) +12secs
6.  Bob Jungels (Lux/Quick-Step) Same time
7.  Jose Goncalves (Por/Katusha) +13secs
8.  Ruben Fernandez (Spa/Movistar) Same time
9.  Michael Albasini (Swi/Orica) +14secs
10. Jonathan Castroviejo (Spa/Movistar)  Same time
Selected others:
16. Simon Yates (GB/Orica) +18secs
39. Chris Froome (GB/Team Sky) +29secs
56. Peter Kennaugh (GB/Team Sky) +53secs
80 Alex Dowsett (GB/Team Sky) +4mins 59secs
102 Ben Swift (Gb)/UAE Team Emirates +9mins 34secs
Switzerland's Stefan Kung won the second stage of the Tour de Romandie after beating breakaway companion Andriy Grivko in a sprint finish.