With their place in the knockout stages on the line tonight, New Zealand rallied to beat the United States 17-10 in their final Pool A game but Baker left the field during the contest with a hamstring injury.
Baker, who scored a try in each of the New Zealand's first two games today, is unlikely to take any further part in the tournament, which opens up a spot for a young gun like Gillies Kaka to start tomorrow.
Had New Zealand lost to the USA they would have missed out on a place in the cup finals and they looked behind the eight ball throughout most of the contest but flashes of brilliance from Tomasi Cama and David Raikuna was enough for the Kiwis to hold on.
Cama bagged a double for New Zealand against the USA while Ben Lam also scored.
England's strong Pool A form saw them register two wins and a draw, which allowed them to progress as the top qualifier from the group with New Zealand in second spot.
Kiwi coach Gordon Tietjens put his side's rusty performances, particularly the opening 19-14 loss to England and the 36-5 win over Spain, down to a lack of match play in recent weeks.
New Zealand's last tournament was in South Africa in early December but the world series took a long break over the Christmas and New Year period.
"They're just real rusty. That gap between when we played our last two tournaments and this is huge," Tietjens said following his side's win over Spain.
"This is huge the work you do between and perhaps we need more games together so it's pretty tough and even in our second game against Spain, while it may have been convincing in the end, it certainly wasn't competent the way we played. There were still a lot of areas where our accuracy's just not where it should be."
New Zealand's young bucks were impressive during the second spell of the victory against Spain and Rocky Khan and Luke Masirewa were particularly sharp.
"That's what you want from the bench," Tietjens said.
"You can never underestimate any of the teams and I think we probably just couldn't get up for the first one like we should have. But give some credit to England because they're a good side, they've got a lot of firepower in there as well but we were up against a good defence. But we turned that around and we still put 30-odd points on Spain and Spain's a team that has beaten England in the past."
New Zealand lead the world series standings after three rounds and are two-time defending champions in the Wellington leg.
Tietjens said his side needed to click during the rest of the weekend if they wanted to achieve a three-peat in the capital for the second time after they won a hat-trick of tournaments between 2003 and 2005.
"We've got dominate when we've got the ball in contact, [get] quick ball and dominate and that's probably the real area for us. It's also about defence, which is where you dominate in the tackle, post tackle and give them the go forward, that's really key in sevens because the quality of possession and the amount of possession is massive."
The first day of the tournament threw out a few upsets with Fiji failing to make the cup quarter-finals for the first time in 14 years on the international circuit.
Kenya were the surprise package of the day as they won their three group games to top Pool B, while Argentina finished second in the group.
Samoa went unbeaten in Pool C and moved through to the knockout stages with South Africa, while Australia and Scotland qualified for the quarter-finals from Pool D.
Action gets underway tomorrow at 1pm and New Zealand meet Australia in their quarter-final at 3.17pm with the cup final due to be played at 9.30pm.
