Ospreys outside half Sam Davies got the first points of the day with a penalty in the first minute and Blues centre Evans ran in his first try after 16 minutes for Davies to convert. However, a failure to capitalise on scoring opportunities allowed Italy back into the game and scrum half Simone Marinaro claimed a try after 23 minutes to cut the lead to 10-5.
After a 17 - 34 loss to France the previous weekend a win was vital for Wales and coaches Gruff Rees and Dale McIntosh gathered the troops at half-time and the side came out with more purpose after the break.
Half backs Davies and Rhodri Williams linked well to stamp their control on proceedings and the Blues centre pairing of Thomas Pascoe and try scorer Evans also impressed. Up front, Wales matched the physical Italian pack and built on that platform with Davies slotting three penalties after the break.
There was no break in the Welsh momentum despite a yellow card for replacement hooker Elliot Dee on 55 minutes, and some impressive build-up work led to Evans' second try.
Prop Rudy Biancotti scored five minutes from time, with a conversion from Edoardo Padovani, but Wales had done enough with the win putting them in second position in their Six Nations pool ahead of the FIRA-AER tournament in France at Easter.
Head coach Gruff Rees said, "We are satisfied with the win, we needed to do a job after losing so disappointingly to France last weekend. Considering the difficult conditions, we are pleased with the performance, especially given the point at which we started the week.
"We worked hard in preparation for the games and we are pleased with our improved defensive display - neither of the two Italian tries came from line breaks - and from a spatial and communications point of view, we were much better. However, there is still a long way to go with this side and we have time now to prepare to play Scotland next month before heading to France."
Wales Scorers: Tries: Ryan E Evans 2; Cons: Sam Davies 2; Pens: Sam Davies 4
Cory Allen (Blues / Glam Wands / Y Fro); Jack Randall (Scarlets / Ammanford / Amman Valley), Ryan E Evans (Blues/ Tonyrefail/ Tonyrefail comp), Thomas Pascoe (Blues / Mountain Ash / Coleg Morgannwg), Owen Jenkins (Blues/ Ynysybwl / Pontypridd High); Sam Davies (Ospreys / Gorseinon / Gowerton Comp), Rhodri Williams (vice-capt, Scarlets/ Llandovery / Amman Valley Comp); Thomas Davies (Blues / Ystrad Rhondda/ Ferndale Community School) Jack Dando (Blues / Penygraig / Coleg Morgannwg), Bradley Thyer (Blues / Ystrad Rhondda / Ferndale), Jack Jones (Ospreys / Llandovery Coll), Rhodri Hughes (Ospreys / Hendy / Gwyr), Ieuan Jones (Dragons / Bargoed Youth), Ellis Jenkins (capt, Blues / Llantwit Fardre / Bryn Celynog), Lewis Young (Blues/ Coleg Morgannwg).
Replacements: Elliot Dee (Dragons/ Penallta / Newbridge Comp), Nicky Smith (Ospreys / Gower College), Daniel Suter (Ospreys / Tonmawr / Neath Port Talbot Coll), Llywelyn Jones (Scarlets/ Haverfordwest / Thomas Picton), Sion Bennett (Scarlets/ Coleg Sir Gar / Narberth),Rhys Patchell (Blues/ CHSOB / Glantaf), Jordan Williams (Scarlets / Llanelli / Coleg Sir Gar)