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Dover slipped to the foot of the National League after a bitterly disappointing home defeat on Saturday.
Solihull striker Jermaine Hylton broke the deadlock 18 minutes from time and Danny Wright swiftly added a second to leave Whites without a win in seven matches.
They have won just once in 11 games and the pressure appears to be mounting on Chris Kinnear, whose side were top this time last year. This was their fourth defeat in six matches at Crabble this season.
The Whites side showed four changes from that which had drawn 0-0 at Chestfield last week with Josh Passley and Jamie Allen injured and Aryan Tajbakhsh suspended. Jack Connors dropped to the bench and in came George Smith, Ejiro Okosieme, Nortei Nortey and Kadell Daniel.
They made a bright start, with loan signing Smith sending in an early cross which caused problems before shooting straight at Moors keeper Ryan Boot after a surging run when perhaps he had better options.
The home side looked to use the pace of Tobi Sho-Silva, Anthony Jeffrey and Daniel to get in behind the Solihull defence but the trio lacked the physical presence to cause any real problems.
The game's first shot on target came from Solihull's Kwame Thomas who forced Mitch Walker to save away to his left on 18 minutes, by which time the visitors had already been forced into a change with Luke Maxwell going off to be replaced by Corey O'Keeffe.
Okosieme, making his first start, almost gave Whites the lead midway through the half when he rose well to meet Daniel's corner only for his header to clip the top of the crossbar.
Solihull's Jamey Osborne fired well wide from 20 yards but in truth goalmouth action was at a premium in a scrappy first half which produced bookings for Dover's Essam and Solihull's Darren Carter, both for fouls.
Both sides resisted the temptation to make changes at half-time and after a slow start Whites created a opening on 54 minutes when Jeffrey's cross just eluded the head of Daniel as he came flying in.
Solihull keeper Ryan Boot was forced into his first save on the match, on 61 minutes when he dived to his left to parry Nortei Nortey's 25-yard drive and soon after Moussa Diarra produced a great block as Moors Thomas looked to turn in Wright's low cross.
Whites replaced Sho-Silva with Inih Effiong midway through the half, but it was the visitors who broke the deadlock not long after.
O'Keeffe's cross was only cleared as far as Carter whose header put Hylton in the clear and he beat Walker with a lob that the keeper got a hand to but could not keep out.
The killer second arrived on 78 minutes when Wright fired home after making room for a shot from the edge of the area.
Dover substitute David Smith then fired straight at Boot who also saved well from Effiong but Solihull almost added insult to injury when Walker did well to save with his foot from Yussuf.
Dover: Walker, Okosieme, G. Smith, Schmoll, Essam, Diarra, Brundle, Nortey, Jeffrey (D.Smith 77mins), Sho-Silva (Effiong 67mins), Daniel; Subs: Fazakerley, Connors,Massanka.
Solihull: Boot, Williams, Daly, Gudger, Osborne (Murphy 90mins), Carter, Hylton (Yussuf 85mins), Carline, Thomas, Maxwell (O'Keeffe 16mins), Wright; Subs:Sweeney, Tibbetts.
Attendance: 823