After all their good defensive work in the first-half, Quins then went behind thanks to a missed tackle. Marcus Smith was unable to contain Butt in midfield, with the centre scampering up the pitch to add the Chiefs’ third.
Schmid’s close-range effort restored parity, with the number eight then capitalising minutes later to add another.
Following strong carrying from Sam Riley and Luke Northmore, Quins drove into the Chiefs’ 22. With the ball eventually recycled wide, the back-rower drove through the final defenders to score in the corner.
Following late tries for Kenningham and Woodburn, the Chiefs found themselves only three points behind, but with the clock in the red they lost the ball at the lineout allowing Quins to kick for touch to record only their second league victory of the season.
Exeter: Haydon-Wood; Feyi-Waboso, Slade, Butt, Woodburn; Skinner, Varney; Abuladze, Yeandle (c), Iosefa-Scott; Pearson, Wilson, Roots, Vintcent, Fisilau.
Replacements: Norey, Goodrick-Clarke, Tchumbadze, Bailey, James, Wolstenholme, Hammersley, Wimbush.
Harlequins: Furbank; David, Northmore, Bradley, Murley (c); Smith, Porter; Baxter, Walker, Kerrod; Dun, Treadwell, Kenningham, Driscoll, Schmid.
Replacements: Riley, Hobson, Streeter, Williams, Browne, Evans, Friday, Isgro.
Yellow card: Bradley (24).
Referee: Joe James.