Tumor invasion within the interstitial space is critically regulated by the force balance between cell-extracellular matrix (ECM) and cell-cell interactions. Interstitial flows (IFs) are present in both healthy and diseased tissues. However, the roles of IFs in modulating cell force balance and subsequently tumor invasion are understudied. In this article, we develop a microfluidic model in which tumor spheroids are embedded within 3D collagen matrices with well-defined IFs. Using co-cultured tumor spheroids (1:1 mixture of metastatic and non-tumorigenic epithelial cells), we show that IFs downregulate the cell-cell adhesion molecule E-cadherin on non-tumorigenic cells and promote tumor invasion. Our microfluidic model advances current tumor invasion assays towards a more physiologically realistic model using tumor spheroids instead of single cells under perfusion. We identify a novel mechanism by which IFs can promote tumor invasion through an influence on cell-cell adhesion within the tumor and highlight the importance of biophysical parameters in regulating tumor invasion.