Lanzini appeared to pull his hamstring in the second half at the London Stadium, and was replaced by Javier Hernandez, who scored the leveller for West Ham two minutes after Ryan Fraser's 71st-minute opener.
West Ham have lost just once in their last six and are unbeaten in five in the Premier League, leaving them 11th in the table.
West Ham certainly set about their task with a sense of urgency, pinning the visitors back under sustained early pressure.
Begovic again came to the Cherries' rescue before the hour mark when he parried James Collins' glanced header away from the chasing Lanzini, while Arnautovic failed to make the most of a one-on-one opportunity by getting the ball stuck under his feet, granting Steve Cook time to race in for a recovery challenge. "We're short on the bench at the moment, we've got a lot of injuries". "We're working hard and we'll keep trying to get someone".
Javier Hernandez is reportedly close to completing a move to Besiktas
Hernandez levelled 69 seconds later with an opportunist close-range goal, bundling the ball past goalkeeper Asmir Begovic after a long ball upfield fell kindly for Marko Arnautovic whose shot was half-blocked. "Today, the boys who have probably been a handful all year just didn't quite get the magic today which we needed from them".
The Turkish side's chairman, Fikret Orman is in London and holding advanced talks with West Ham regarding Chicharito.
The Scotsman though Tuesday evenings extra-time Emirates FA Cup exploits might have had an effect on his side, adding: "With fifteen minutes to go I would have taken a draw because I thought we were on our knees".
"We won't to look there, but we're mindful that it won't take too much to slip down".
Four US, Canadian captives freed in Nigeria
The gunmen are reported by Nigeria's Vanguard newspaper to have killed two Nigerian policemen who were escorting the foreigners. This was even as it said two of the Kidnappers have been arrested and now helping the police in its investigation.