Ecuador grabbed an eighth minute lead through a thundering header from Enner Valencia before England drew level in the 29th minute with Rooney poking home after a scramble in the area.
Midfielder Ross Barkley produced a moment of fine individual skill to set up Lambert for a sweet strike in the 51st minute, but Ecuador fought back with a thundering drive from Michael Arroyo.
The double red cards came after a wild challenge from England substitute Raheem Sterling on Antonio Valencia.
The Ecuadorian winger, who plays for Manchester United, retaliated by grabbing the neck of the Liverpool youngster and American referee Jair Marrufo brandished two red cards.
Rooney was the only player named who started Friday’s 3-0 win over Peru at Wembley Stadium as Roy Hodgson experimented with his options.
The Manchester United forward started on the left flank, not considered his favourite role, with Lambert, recently signed by Liverpool, at centre-forward.
“It was a very young line-up but I thought we acquitted ourselves quite brilliantly and played some very good football at times,” Hodgson said.
“I was happy for (Wayne) that he scored his goal and both him and Frank Lampard, as the only two on the pitch with any significant number of caps, took their responsibility ever so well.
“They helped see us through what, in my opinion, is quite a well-merited and prestigious draw against a strong Ecuadorian team.”
Ecuador also made five changes from the team which lost 3-1 to Mexico in Dallas on Saturday as they looked to improve on a recent run of form ahead of their tests in Group E against France, Honduras and Switzerland.
The South Americans started brightly, exposing the unfamiliarity of England’s back four, and they took the lead in just the eighth minute.
Walter Ayovi whipped in a fine cross from the left flank and Enner Valencia rose superbly, beating Chris Smalling to the ball and powering in a header to make it 1-0.
England responded positively though, Rooney looping a ball into the area to the over-lapping Luke Shaw’s whose shot was pushed out by Ecuador keeper Maximo Baguera.
But Ecuador continued to probe England’s shaky looking defence – Carlo Gruezo wriggling himself into some space and firing in a low shot in the 16th minute which England keeper Ben Foster did well to keep out.
England’s approach with the ball was patient and possession-based and after a long spell of short passes captain Frank Lampard tested Banguera with a well-struck effort from 30 metres out.
While much of England’s play was pretty, if lacking penetration, when their equaliser came it was scrappy and fortunate.
Alex Oxlade-Chamberlain’s low cross was fumbled by the diving Banguera and in the resulting scramble, Lambert back-heeled against the post and Rooney prodded home the loose ball.
It was a solid first 45 minutes from England albeit one which hardly set the pulse racing while Ecuador looked much more confident than in some of their recent displays.
If there was a player who had brought flashes of pace and invention to England’s performance it was Everton midfielder Barkley, and it was the 20-year-old who produced a moment of skill to give his team the lead, five minutes after the re-start.
Brilliant footwork from Barkley took him away from Jorge Guagua and he burst towards goal, leaving two Ecuador defenders standing, before slipping the ball perfectly into the path of Lambert who cracked home a low angled drive into the far corner.
There was injury worry for Hodgson when Oxlade-Chamberlain limped off in the 63rd minute with possible knee ligament damage, and Rooney was rested two minutes later with Liverpool forward Sterling introduced.
Ecuador should have drawn level a few minutes after those changes when Joao Rojas broke free down the left and slipped a pass to goalscorer Enner Valencia but from a great position he scuffed his shot against the post.
When the equaliser came though it was in spectacular fashion – substitute Michael Arroyo blasting, from the edge of the box, an unstoppable drive into the top corner past a helpless Foster.
Then came the clash between Sterling and Antonio Valencia, an unpleasant end to an entertaining warm-up for Brazil.
England will face Italy, Costa Rica and Uruguay in Group D.