He began his career as a soloist under the direction of conductors such as Claudio Abbado, Eliahu Inbal, Peter Maag and Giuseppe Sinopoli, performing in prestigious concert halls.
Among other recordings are the Grieg Concerto in A minor and Richard Strauss Burleske in D minor with the London Philharmonia and Jean-Bernard Pommier, a "live" recording of the Schumann Concerto at the Vienna Festival with the Wiener Symphoniker and Eliahu Inbal, songs by Chausson with Jessye Norman and two recitals with Barbara Hendricks.
Reaching beyond Switzerland from the 1930s, the fame of the orchestra later attracted guest conductors including Bruno Walter, Wilhelm Furtwängler, Ernest Ansermet, Hans Knappertsbusch, Ferenc Fricsay, Rafael Kubelík, Günter Wand, Kurt Sanderling, Horst Stein, Yuri Ahronovitch and Eliahu Inbal.
As a soloist, Gawriloff has played with many prestigious orchestras around the world, led by such conductors as Georg Solti, Pierre Boulez, Christoph von Dohnányi, Eliahu Inbal, Michael Gielen, Esa-Pekka Salonen, Markus Stenz, Peter Eötvös, Gary Bertini, and Alfred Schnittke.