Compton, who flopped in the first two innings that he played on the tour by scoring a duck (against India A in the opener at the Brabourne Stadium) and one (in the first innings here), started nervously before helping himself to some form.
England, who made 345 for nine declared in the first innings, were 149 for two wickets in 52 overs in the second when play was called off.
When stumps were drawn for the last time, Compton was unbeaten with 64 after a stay of 214 minutes during which he faced 162 balls and hit 6 fours.
Ian Bell (28), who faced 42 balls and hit three fours in 58 minutes, was the batsman who was not out at the other end.
The England pace bowlers did not do anything extraordinary in the match barring bowling long spells, with James Anderson and Graham Onions procuring one and two wickets respectively.
Stand-in skipper Stuart Broad could not do that too because of a left heel injury that restricted him to bowl 10 overs, while Panesar showed he could trouble the Indian batsmen with some help from the track.
Patel was a big gainer and staked strong claims to grab a middle order slot with his knock of 60 and followed it up today by claiming three wickets in 16 balls as Mumbai A slumped from overnight 232 for 4 to being all out in 93 minutes.