Eastleigh extended their lead at the top of the table thanks to Phil Warner's first goal for the club - but Blackfield & Langley made it difficult.
Right-back Warner sidefooted home the only goal of the afternoon on 51 minutes with the aid of a deflection.
Boss Paul Doswell admitted: "I had to lock them in the dressing room for half an hour afterwards. I can't remember us playing as badly but you have to give some credit to Blackfield.
"They had some good chances and deserved something from the game but it turned out to be a good weekend for us because of Gosport's defeat.
"When I got that result as a text message in the dressing room it took the sting out of the rollicking I was giving the players and also cost me a £5 fine, but it was a good fiver.
"We've played badly and have extended our lead at the top.
"That's the sign of a good team but Phil's goal was scrappy - typical of the match."
Blackfield boss Terry Smith insisted his lowly side deserved a shock point.
"It was a tremendous all-round performance from every single one of my players," he said.
"A fair result would have been a draw. We didn't let them play football at all - we harried and chased them all afternoon.
"That was the gameplan. We knew if we let them play football we would be in trouble."
Blackfield created a couple of chances late on, but visiting keeper Colin Matthews wasn't seriously tested.
Young Danny Sharazi broke through "but ran out of puff" according to his manager, while substitute Danny Moggeridge shot straight at Matthews.
Smith insists his players have now set a new benchmark in terms of effort that must be replicated when they play sides from the lower end of the table.
"We've got the likes of Whitchurch and Brockenhust coming up and if we perform like we did against Eastleigh then we should be moving up the table," he admitted.
Reserve keeper Greg Livermore will play at Wimborne next Saturday as regular No 1 Tom Hawkins was today due to start a 35-day suspension.
Hamble boss Larry Clay said he was "gutted" after Steve McNulty's 90th-minute decider had given Andover a 2-1 success.
"It was a good end-to end-match," he said.
"I thought we were worth a point, but their second goal was on the cards because they really attacked us in the last 15 minutes."
Danny Sullivan had given Andover a 26th-minute lead, capitalising on a Hamble defensive mix-up, only for Rob Ackroyd to level with a 30-yard drive from a free-kick in the 63rd minute.
Hamble thought they should have had a penalty in the second half when Joe Partridge was fouled. "It was blatant," said Clay, "but typical of our luck."
