The Hammers, beaten 3-0 at Aston Villa last week, now head into Premier League fixtures against Manchester United and Chelsea rooted in the bottom three without a single point.
Bolton weathered a first-half storm - including a missed penalty from Hammers striker Carlton Cole - before snatching the lead with a Matthew Upson own goal.
Johan Elmander wrapped up the points with strikes either side of a Mark Noble penalty as Bolton extended their winning run over West Ham to seven matches.
West Ham were booed from the field and they could conceivably head into the game against Stoke on September 18 without a point on the board.
Hammers manager Grant said: "We have a very tough two games. If you saw the spirit today after the game last week, this team this season is not going to give up.
"I am happy how players responded. The defence was good, we pushed forward, we played high, we created a lot of chances.
"On the football side everything went well. We played like a team at the top. I am very happy with the performance, I am very disappointed with the result.
"It was a strange game."
Grant insisted Upson was pushed by striker Kevin Davies in the process of scoring the own goal that gave Bolton the upper hand.
Upson seemed to stoop to head the ball past Robert Green - and in the process he received a boot in the face from Davies and had to go off.
"There was a clear foul on the first goal. We know they play direct ball - Matthew was in the right place, he was before Davies who pushed him. The referee needs to be more awake," said Grant.
"He smashed his face. He cannot have an x-ray now."
Bolton manager Owen Coyle conceded that on another day West Ham could have been in charge at half-time.
But Coyle revealed his side's recent dominance over the Hammers played a big part in reinforcing their belief that another Upton Park win was there for the taking.
"I wish it was a two-team league," joked Coyle.
"Sometimes as a player there are teams you are suited to play against. We were aware of that and we had a belief we could win the game.
"We did it last year and I think we have improved since then.
"We were in charge for the first 10-15 minutes but after that West Ham really got at us. Jussi Jaaskelainen had to be in top form which he was, he made some terrific saves.
"We had to get them in at half-time to regroup, we had one or two things to say. In the second half we really showed our quality. We scored two very good goals.
"At 2-0 when we looked so comfortable we had to withstand some pressure after the referee awarded a second penalty, which I think we all agree wasn't a penalty.
"The lads showed great character and scored again. It was hard work - it was a terrific game end to end - and I am delighted with the three points."
Elmander has only scored 10 goals in 57 appearances for Bolton but Coyle said: "I am a great believer in Elmander. Last week I said if he kept giving that level of performance the goals would go in.
"He will take confidence from that today. He is a great lad and a very good player but only Johan can determine that when he crosses the white line.
"I thought him and Kevin were a real handful for West Ham today."