Put into bat, Indians lost their openers early with Shikhar Dhawan (10) and Rohit Sharma (8) falling to the Middlesex new-ball bowlers Gurjit Sandhu (1-65) and Steven Finn (1-20) respectively.
Ajinkya Rahane (14) also could not last long as the No.4 batsman fell to medium-pacer James Harris (1-29).
Leading the Indians, Kohli (71) then got going with Rayudu (72 retired out) to stitch a fourth-wicket 104-run partnership and put the innings back on track. It was good to see under-fire Kohli back amongst runs after a poor Test series.
The Middlesex spinners then turned on the heat. Left-arm orthodox bowler Ravi Patel (2-56) sent Kohli packing in the 30th over and Ravindra Jadeja (7) in the 34th.
Off-spinner Olliver Rayner (4-32) soon took over from Patel to bag four wickets as Ravichandran Ashwin (18), Sanju Samson (6), Stuart Binny (0) and Suresh Raina (5), who came in at No.11, fell to his guile.
In the only practice game before the five-match one-day series starting on Monday, the Indians have been allowed to play their 17 players with 11 batsmen and 11 fielders while the David Malan-led Middlesex are playing with 13 players, 11 batsmen and 11 fielders.